Peter Olver's Papers, Preprints, etc.

Last updated:   April 7, 2013

Moving Frames, Equivalence, and Pseudo-group Papers

  1. Olver, P.J., Recursive moving frames, Results Math. 60 (2011), 423-452.   pdf
  2. Olver, P.J., Recent advances in the theory and application of Lie pseudo-groups, in: XVIII International Fall Workshop on Geometry and Physics, M. Asorey, J.F. Cariñena, J. Clemente-Gallardo, and E. Martínez, AIP Conference Proceedings, vol. 1260, American Institute of Physics, Melville, NY, 2010, pp. 35-63.   pdf
  3. Olver, P.J., Differential invariant algebras, Comtemp. Math. 549 (2011), 95-121.   pdf
  4. Olver, P.J., and Pohjanpelto, J., Persistence of freeness for pseudo-group actions, Arkiv Mat. 50 (2012), 165-182.   pdf
  5. Olver, P.J., Moving frames and differential invariants in centro-affine geometry, Lobachevsky J. Math. 31 (2010), 77-89.   pdf
  6. Itskov, V., Olver, P.J., and Valiquette, F., Lie completion of pseudo-groups, Transformation Groups 16 (2011), 161-173.   pdf
  7. Mari-Beffa, G., and Olver, P.J., Poisson structures for geometric curve flows on semi-simple homogeneous spaces, Regular and Chaotic Dynamics 15 (2010), 532-550.   pdf
  8. Olver, P.J., Pohjanpelto, J., and Valiquette, F., On the structure of Lie pseudo-groups, SIGMA 5 (2009), 077.   pdf
  9. Olver, P.J., Lectures on moving frames, in: Symmetries and Integrability of Difference Equations, D. Levi, P. Olver, Z. Thomova, and P. Winternitz, eds., London Math. Soc. Lecture Note Series, vol. 381, Cambridge University Press, Cambridge, 2011, pp. 207-246.   pdf
  10. Olver, P.J., Differential invariants of maximally symmetric submanifolds, J. Lie Theory 19 (2009), 79-99.   pdf
  11. Olver, P.J., Invariant variational problems and invariant flows via moving frames, in: Variations, Geometry and Physics, O. Krupková, and D. Saunders, eds., Nova Science Publ., New York, 2009, pp. 209-235.   pdf
  12. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008), 344017.   Corrected version: pdf   Corrections to published version: pdf
  13. Olver, P.J., and Pohjanpelto, J., Differential invariant algebras of Lie pseudo-groups, Adv. in Math. 222 (2009), 1746-1792.   Corrected version: pdf   Corrections to published version: pdf
  14. Hubert, E., and Olver, P.J., Differential invariants of conformal and projective surfaces, SIGMA 3 (2007), 097.   pdf
  15. Olver, P.J., and Pohjanpelto, J., Moving frames and differential invariants for Lie pseudo-groups, in: Symmetry and Perturbation Theory, G. Gaeta, R. Vitolo, and S. Walcher, eds., World Scientific, Singapore, 2007, pp. 172-180.   pdf
  16. Kamran, N., Olver, P.J., and Tenenblat, K., Local symplectic invariants for curves, Commun. Contemp. Math. 11 (2009), 165-183.   pdf
  17. Olver, P.J., Differential invariants of surfaces, Diff. Geom. Appl. 27 (2009), 230-239.   pdf
  18. Olver, P.J., and Pohjanpelto, J., Differential invariants for Lie pseudo-groups, in: Gröbner Bases in Symbolic Analysis; M. Rosenkranz, D. Wang, eds, Radon Series Comp. Appl. Math., vol. 2, Walter de Gruyter, Berlin, 2007, pp. 217-243.   pdf
  19. Olver, P.J., and Pohjanpelto, J., Pseudo-groups, moving frames, and differential invariants, in: Symmetries and Overdetermined Systems of Partial Differential Equations, M. Eastwood and W. Miller, Jr., eds., IMA Volumes in Mathematics and Its Applications, vol. 144, Springer-Verlag, New York, 2008, pp. 127-149.   pdf
  20. Cheh, J., Olver, P.J., and Pohjanpelto, J., Algorithms for differential invariants of symmetry groups of differential equations, Found. Comput. Math. 8 (2008), 501-532.   pdf
  21. Olver, P.J., and Pohjanpelto, J., Moving frames for Lie pseudo-groups, Canadian J. Math. 60 (2008), 1336-1386.   pdf
  22. Olver, P.J., Generating differential invariants, J. Math. Anal. Appl. 333 (2007), 450-471.   pdf
  23. Welk, M., Kim, P., and Olver, P.J., Numerical invariantization for morphological PDE schemes, in: Scale Space and Variational Methods in Computer Vision, F. Sgallari, A. Murli, and N. Paragios, eds., Lecture Notes in Computer Science, vol. 4485, Springer-Verlag, New York, 2007, pp. 508-519.   pdf
  24. Olver, P.J., and Pohjanpelto, J., Maurer-Cartan forms and the structure of Lie pseudo-groups, Selecta Math. 11 (2005), 99-126.   pdf
  25. Lewis, D., Nigam, N., and Olver, P.J., Connections for general group actions, Commun. Contemp. Math. 7 (2005), 341-374.   pdf
  26. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, H. Li, P.J. Olver, and G. Sommer, eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.   pdf
  27. Olver, P.J., and Pohjanpelto, J., Regularity of pseudogroup orbits, in: Symmetry and Perturbation Theory, G. Gaeta, B. Prinari, S. Rauch-Wojciechowski, and S. Terracini, eds., World Scientific, Singapore, 2005, pp. 244-254.   pdf
  28. Cheh, J., Olver, P.J., and Pohjanpelto, J., Maurer-Cartan equations for Lie symmetry pseudo-groups of differential equations, J. Math. Phys., 46 (2005), 023504.   pdf
  29. Kim, P., and Olver, P.J., Geometric integration via multi-space, Regular and Chaotic Dynamics 9 (2004), 213-226.   pdf
  30. Olver, P.J., An introduction to moving frames, in: Geometry, Integrability and Quantization; vol. 5, I.M. Mladenov, and A.C. Hirschfeld, eds., Softex, Sofia, Bulgaria, 2004, pp. 67-80.   pdf
  31. Olver, P.J., Moving frames, J. Symb. Comp. 36 (2003), 501-512.   pdf
  32. Olver, P.J., Moving frames: a brief survey, in: Symmetry and Perturbation Theory, D. Bambusi, M. Cadoni, and G. Gaeta, eds., World Scientific, Singapore, 2001, pp. 143-150.   pdf
  33. Kogan, I., and Olver, P.J., Invariant Euler-Lagrange equations and the invariant variational bicomplex, Acta Appl. Math. 76 (2003), 137-193.   Corrected version: pdf   Corrections to published version: pdf
  34. Kogan, I., and Olver, P.J., The invariant variational bicomplex, Contemp. Math. 285 (2001), 131-144.   Corrected version: pdf   Corrections to published version: pdf
  35. Olver, P.J., The canonical contact form, Adv. Studies Pure Math. 37 (2002), 267-285   pdf
  36. Olver, P.J., Geometric foundations of numerical algorithms and symmetry, Appl. Alg. Engin. Comp. Commun. 11 (2001), 417-436.   pdf
  37. Olver, P.J., Moving frames — in geometry, algebra, computer vision, and numerical analysis, in: Foundations of Computational Mathematics, R. DeVore, A. Iserles, and E. Suli, eds., London Math. Soc. Lecture Note Series, vol. 284, Cambridge University Press, Cambridge, 2001, pp. 267-297.   pdf
  38. Olver, P.J., Joint invariant signatures, Found. Comput. Math. 1 (2001), 3-67.   pdf
  39. Fels, M., and Olver, P.J., Moving frames and moving coframes, in: Algebraic Methods in Physics, Y. Saint-Aubin and L. Vinet, eds., CRM Series in Math. Phys., Springer-Verlag, New York, 2001, pp. 47-64.   pdf
  40. Olver, P.J., Moving frames, RIMS Kokyuroku 1150 (2000), 114-124.   pdf
  41. Olver, P.J., Moving frames and singularities of prolonged group actions, Selecta Math. 6 (2000), 41-77.   pdf
  42. Berchenko, I., and Olver, P.J., Symmetries of polynomials, J. Symb. Comp. 29 (2000), 485-514.   pdf
  43. Olver, P.J., Moving frames and joint differential invariants, Regular and Chaotic Dynamics 4 (4) (1999), 3-18.   pdf
  44. Mari-Beffa, G., and Olver, P.J., Differential invariants for parametrized projective surfaces, Commun. Anal. Geom. 7 (1999), 807-839.   pdf
  45. Fels, M., and Olver, P.J., Moving coframes. II. Regularization and theoretical foundations, Acta Appl. Math. 55 (1999), 127-208.   Corrected version: pdf   Corrections to published version: pdf
  46. Fels, M., Olver, P.J., Moving coframes. I. A practical algorithm, Acta Appl. Math. 51 (1998), 161-213.   Corrected version: pdf   Corrections to published version: pdf
  47. Fels, M., and Olver, P.J., On relative invariants, Math. Ann. 308 (1997), 701-732.   pdf
  48. Olver, P.J., Pseudo-stabilization of prolonged group actions. I. The order zero case, J. Nonlinear Math. Phys. 4 (1997), 271-277.   pdf
  49. Olver, P.J., Differential invariants, Acta Applicandae Math. 41 (1995), 271-284.   pdf
  50. Olver, P.J., Differential invariants and invariant differential equations, Lie Groups and their Appl. 1 (1994), 177-192.   pdf
  51. Olver, P.J., Equivalence and the Cartan form, Acta Applicandae Math. 31 (1993), 99-136.   pdf
  52. Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians III. New invariant differential equations, Nonlinearity 5 (1992), 601-621.   pdf
  53. Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians I. Formulation and reduction, J. Math. Pures et Appliquees 70 (1991), 369-391.   pdf
  54. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians. I. Binary Forms, Adv. in Math. 80 (1990), 39-77.   pdf
  55. Olver, P.J., Invariant theory, equivalence problems and the calculus of variations, in: Invariant Theory and Tableaux, D. Stanton, ed., IMA Volumes in Mathematics and Its Applications, vol. 19, Springer-Verlag, New York, 1990, pp. 59-81.   pdf
  56. Hsu, L., Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians II. The Cartan form for particle Lagrangians, J. Math. Phys. 30 (1989), 902-906.   pdf
  57. Kamran, N., and Olver, P.J., Le probleme d'equivalence a une divergence pres dans le calcul des variations des integrales multiples, Comptes Rendus Acad. Sci. (Paris), Serie I, 308 (1989), 249-252.   
  58. Kamran, N., and Olver, P.J., Equivalence of differential operators, SIAM J. Math. Anal. 20 (1989), 1172-1185.   pdf
  59. Kamran, N., and Olver, P.J., Equivalence problems for first order Lagrangians on the line, J. Diff. Eq. 80 (1989), 32-78.   pdf
  60. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians, Bull. Amer. Math. Soc. 18 (1988), 21-26.   pdf
  61. Olver, P.J., The equivalence problem and canonical forms for quadratic Lagrangians, Adv. Appl. Math. 9 (1988), 226-257.   pdf

Computer Vision Papers

  1. Hoff, D., and Olver, P.J., Automatic solution of jigsaw puzzles, preprint, University of Minnesota, 2011.   pdf   Matlab routines
  2. Hoff, D., and Olver, P.J., Extensions of invariant signatures for object recognition, J. Math. Imaging Vision 45 (2013), 176-185.   pdf   Matlab routines
  3. Brinkman, D., and Olver, P.J., Invariant histograms, Amer. Math. Monthly 119 (2012), 4-24.   pdf
  4. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008), 344017.   Corrected version: pdf   Corrections to published version: pdf
  5. Welk, M., Kim, P., and Olver, P.J., Numerical invariantization for morphological PDE schemes, in: Scale Space and Variational Methods in Computer Vision, F. Sgallari, A. Murli, and N. Paragios, eds., Lecture Notes in Computer Science, vol. 4485, Springer-Verlag, New York, 2007, pp. 508-519.   pdf
  6. Rathi, Y., Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant surface evolutions for 3D image segmentation, in: Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning, E.R. Dougherty, J.T. Astola, K.O. Egiazarian, N.M. Nasrabadi, and S.A. Rizvi, eds., vol. 6064, SPIE Press, Bellingham, Wash., 2006, pp. 606401.   pdf
  7. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, H. Li, P.J. Olver, and G. Sommer, eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.   pdf
  8. Georgiou, T., Olver, P.J., and Tannenbaum, A., Maximal entropy for reconstruction of back projection images, in: Mathematical Methods in Computer Vision, P.J. Olver and A. Tannenbaum, eds., IMA Volumes in Mathematics and its Applications, vol. 133, Springer-Verlag, New York, 2003, pp. 57-64.   pdf
  9. Olver, P.J., Moving frames — in geometry, algebra, computer vision, and numerical analysis, in: Foundations of Computational Mathematics, R. DeVore, A. Iserles, and E. Suli, eds., London Math. Soc. Lecture Note Series, vol. 284, Cambridge University Press, Cambridge, 2001, pp. 267-297.   pdf
  10. Calabi, E., Olver, P.J., Shakiban, C., Tannenbaum, A., and Haker, S., Differential and numerically invariant signature curves applied to object recognition, Int. J. Computer Vision 26 (1998), 107-135.   Corrected version: pdf   Corrections to published version: pdf
  11. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P.J., and Tannenbaum, A., A geometric snake model for segmentation of medical imagery, IEEE Trans. Medical Imaging 16 (1997), 199-209.   pdf
  12. Olver, P.J., Sapiro, G., and Tannenbaum, A., Invariant geometric evolutions of surfaces and volumetric smoothing, SIAM J. Appl. Math. 57 (1997), 176-194.   pdf
  13. Calabi, E., Olver, P.J., and Tannenbaum, A., Affine geometry, curve flows, and invariant numerical approximations, Adv. in Math. 124 (1996), 154-196.   Corrected version: pdf   Correction to published version: pdf
  14. Kichenassamy, S., Kumar, A., Olver, P.J., Tannenbaum, A., and Yezzi, A., Conformal curvature flows: from phase transitions to active vision, Arch. Rat. Mech. Anal. 134 (1996), 275-301.   pdf
  15. Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant gradient flows, in: ICAOS '96: Images, Wavelets and PDE's, M.-O. Berger, et. al., eds., Lecture Notes in Control and Information Sciences, vol. 219, Springer-Verlag, New York, 1996, pp. 194-200.   pdf
  16. Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant detection: edge maps, anisotropic diffusion, and active contours, Acta Appl. Math. 59 (1999), 45-77.   pdf
  17. Olver, P.J., Sapiro, G., and Tannenbaum, A., Affine invariant detection: edges, active contours, and segments, in: Proceedings 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Proceedings, IEEE Computer Soc. Press, Los Alamitos, CA, 1996, pp. 520-525.   pdf
  18. Calabi, E., Olver, P.J., and Tannenbaum, A., Invariant numerical approximations to differential invariant signatures, preprint, University of Minnesota, 1995.   pdf
  19. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P., and Tannenbaum, A., A gradient surface evolution approach to 3D segmentation, in: Proceedings of the IS&T's 49th Annual Conference; Society for Imaging Science and Technology, Springfield, Virginia, 1996, pp. 305-307   pdf
  20. Kumar, A., Yezzi, A., Kichenassamy, S., Olver, P.J., Tannenbaum, A., Active contours for visual tracking: a geometric gradient based approach, in: Proceedings of the 34th Conference on Decision and Control, IEEE Computer Soc. Press, Piscataway, N.J., 1995, pp. 4041-4046.   pdf
  21. Kichenassamy, S., Kumar, A., Olver, P.J., Tannenbaum, A., and Yezzi, A., Gradient flows and geometric active contour models, in: Fifth International Conference on Computer Vision, IEEE Computer Soc. Press, Cambridge, Mass., 1995, pp. 810-815.   pdf
  22. Olver, P.J., Sapiro, G., and Tannenbaum, A., Differential invariant signatures and flows in computer vision: a symmetry group approach, in: Geometry-Driven Diffusion in Computer Vision, B.M. Ter Haar Romeny, ed., Kluwer Acad. Publ., Dordrecht, Netherlands, 1994, pp. 255-306.   pdf
  23. Olver, P.J., Sapiro, G., and Tannenbaum, A., Classification and uniqueness of invariant geometric flows, Comptes Rendus Acad. Sci. (Paris), Serie I, 319 (1994), 339-344.   pdf

Numerical Analysis Papers

  1. Chen, G., and Olver, P.J., Numerical simulation of nonlinear dispersive quantization, Discrete Cont. Dyn. Syst. A, to appear.   pdf
  2. Fernandez, O.E., Bloch, A.M., and Olver, P.J., Variational integrators for Hamiltonizable nonholonomic systems, J. Geom. Mech. 4 (2012), 137-163.   pdf
  3. Welk, M., Kim, P., and Olver, P.J., Numerical invariantization for morphological PDE schemes, in: Scale Space and Variational Methods in Computer Vision, F. Sgallari, A. Murli, and N. Paragios, eds., Lecture Notes in Computer Science, vol. 4485, Springer-Verlag, New York, 2007, pp. 508-519.   pdf
  4. Olver, P.J., On multivariate interpolation, Stud. Appl. Math. 116 (2006), 201-240.   Corrected version: pdf   Corrections to published version: pdf
  5. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, H. Li, P.J. Olver, and G. Sommer, eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.   pdf
  6. Lewis, D., Nigam, N., and Olver, P.J., Connections for general group actions, Commun. Contemp. Math. 7 (2005), 341-374.   pdf
  7. Kim, P., and Olver, P.J., Geometric integration via multi-space, Regular and Chaotic Dynamics 9 (2004), 213-226.   pdf
  8. Lewis, D., and Olver, P.J., Geometric integration algorithms on homogeneous manifolds, Found. Comput. Math. 3 (2002), 363-392.   pdf
  9. Olver, P.J., Geometric foundations of numerical algorithms and symmetry, Appl. Alg. Engin. Comp. Commun. 11 (2001), 417-436.   pdf
  10. Olver, P.J., Moving frames — in geometry, algebra, computer vision, and numerical analysis, in: Foundations of Computational Mathematics, R. DeVore, A. Iserles, and E. Suli, eds., London Math. Soc. Lecture Note Series, vol. 284, Cambridge University Press, Cambridge, 2001, pp. 267-297.   pdf
  11. Gunney, B.T.N., Li, Y.A., and Olver, P.J., Solitary waves in the critical surface tension model, J. Engin. Sci.36 (1999), 99-112.   pdf
  12. Calabi, E., Olver, P.J., Shakiban, C., Tannenbaum, A., and Haker, S., Differential and numerically invariant signature curves applied to object recognition, Int. J. Computer Vision 26 (1998), 107-135.   Corrected version: pdf   Corrections to published version: pdf
  13. Calabi, E., Olver, P.J., and Tannenbaum, A., Affine geometry, curve flows, and invariant numerical approximations, Adv. in Math. 124 (1996), 154-196.   Corrected version: pdf   Correction to published version: pdf

Symmetry Papers

  1. Olver, P.J., Differential invariant algebras, Comtemp. Math. 549 (2011), 95-121.   pdf
  2. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008), 344017.   Corrected version: pdf   Corrections to published version: pdf
  3. Cheh, J., Olver, P.J., and Pohjanpelto, J., Algorithms for differential invariants of symmetry groups of differential equations, Found. Comput. Math. 8 (2008), 501-532.   pdf
  4. Muriel, C., Romero, J.L., and Olver, P.J., Variational C∞ symmetries and Euler-Lagrange equations, J. Diff. Eq. 222 (2006), 164-184.   pdf
  5. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, H. Li, P.J. Olver, and G. Sommer, eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.   pdf
  6. Cheh, J., Olver, P.J., and Pohjanpelto, J., Maurer-Cartan equations for Lie symmetry pseudo-groups of differential equations, J. Math. Phys., 46 (2005), 023504.   pdf
  7. Olver, P.J., Lie algebras and Lie groups, in: Encyclopedia of Nonlinear Science, A. Scott, ed., Routledge, New York, New York, 2005, pp. 526-528.   pdf
  8. Olver, P.J., Nonlocal symmetries and ghosts, in: New Trends in Integrability and Partial Solvability, A.B. Shabat et. al., eds., Kluwer Acad. Publ., Dordrecht, Netherlands, 2004, pp. 199-215.   pdf
  9. Kogan, I., and Olver, P.J., Invariant Euler-Lagrange equations and the invariant variational bicomplex, Acta Appl. Math. 76 (2003), 137-193.   Corrected version: pdf   Corrections to published version: pdf
  10. Olver, P.J., Lie groups and differential equations, in: The Concise Handbook of Algebra, A.V. Mikhalev and G.F. Pilz, eds., Kluwer Acad. Publ., Dordrecht, Netherlands, 2002, pp. 92-97.   pdf
  11. Olver, P.J., Sanders, J., and Wang, J.P., Ghost symmetries, J. Nonlinear Math. Phys. 9, Suppl. 1 (2002), 164-172.   pdf
  12. Kogan, I., and Olver, P.J., The invariant variational bicomplex, Contemp. Math. 285 (2001), 131-144.   Corrected version: pdf   Corrections to published version: pdf
  13. Foursov, M.V., Olver, P.J., and Reyes, E.G., On formal integrability of evolution equations and local geometry of surfaces, Diff. Geom. Appl., 15 (2001), 183-199.   pdf
  14. Olver, P.J., Geometric foundations of numerical algorithms and symmetry, Appl. Alg. Engin. Comp. Commun. 11 (2001), 417-436.   pdf
  15. Olver, P.J., Sanders, J., and Wang, J.P., Classification of symmetry-integrable evolution equations, in: Bäcklund and Darboux Transformations. The Geometry of Solitons, A. Coley, D. Levi, R. Milson, C. Rogers and P. Winternitz, eds., CRM Proceedings & Lecture Notes, vol. 29, 2001, pp. 363-372.   pdf
  16. Foursov, M.V., and Olver, P.J., On the classification of symmetrically-coupled integrable evolution equations, in: Symmetries and Differential Equations, V.K. Andreev and Yu.V. Shanko, eds, Institute of Computational Modelling, Krasnoyarsk, Russia, 2000, pp. 244-248.   pdf
  17. Olver, P.J., and Wang, J.P., Classification of integrable one-component systems on associative algebras, Proc. London Math. Soc. 81 (2000), 566-586.   pdf
  18. Kamran, N., Milson, R., and Olver, P.J., Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems, Adv. in Math. 156 (2000), 286-319.   pdf
  19. Olver, P.J., and Sokolov, V.V., Non-abelian integrable systems of the derivative nonlinear Schrödinger type, Inverse Problems 14 (1998), L5-L8.   pdf
  20. Olver, P.J., and Sokolov, V.V., Integrable evolution equations on associative algebras, Commun. Math. Phys. 193 (1998), 245-268.   pdf
  21. Heredero, R.H., Olver, P.J., Classification of invariant wave equations, in: GROUP21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, vol. 2, H.-D. Doebner, W. Scherer, C. Schulte, eds., World Scientific, Singapore, 1997, pp. 1010-1016.   pdf
  22. Heredero, R.H., and Olver, P.J., Classification of invariant wave equations, J. Math. Phys. 37 (1996), 6414-6438.   pdf
  23. Olver, P.J., Non-associative local Lie groups, J. Lie Theory 6 (1996), 23-51.   Corrected version: pdf   Correction to published version: pdf
  24. Clarkson, P.A., and Olver, P.J., Symmetry and the Chazy equation, J. Diff. Eq. 124 (1996), 225-246.   pdf
  25. Olver, P.J., and Vorob'ev, E.M., Nonclassical and conditional symmetries, in: CRC Handbook of Lie Group Analysis of Differential Equations, vol. 3, N.H. Ibragimov, ed., CRC Press, Boca Raton, Fl., 1996, pp. 291-328.   pdf
  26. Olver, P.J., Differential invariants, Acta Applicandae Math. 41 (1995), 271-284.   pdf
  27. Olver, P.J., Differential invariants and invariant differential equations, Lie Groups and their Appl. 1 (1994), 177-192.   pdf
  28. Olver, P.J., Direct reduction and differential constraints, Proc. Roy. Soc. London A 444 (1994), 509-523.   pdf
  29. Anderson, I.M., Kamran, N., and Olver, P.J., Internal, external and generalized symmetries, Adv. in Math. 100 (1993), 53-100.   pdf
  30. Anderson, I.M., Kamran, N., and Olver, P.J., Internal symmetries of differential equations, in: Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, N.H. Ibragimov, M. Torrisi, and A. Valenti, eds., Kluwer, Dordrecht, Netherlands, 1993, pp. 7-21.   
  31. Olver, P.J., and Shakiban, C., Dissipative decomposition of partial differential equations, Rocky Mountain J. Math. 22 (1992), 1483-1510.   pdf
  32. Olver, P.J., Symmetry and explicit solutions of partial differential equations, Appl. Numerical Math. 10 (1992), 307-324.   pdf
  33. Olver, P.J., Internal symmetries of differential equations, in: Differential Equations and Computer Algebra, M. Singer, ed., Academic Press, New York, 1991, pp. 1-28.   
  34. Olver, P.J., Recursion operators and Hamiltonian systems, in: Symmetries and Nonlinear Phenomena, D. Levi and P. Winternitz, eds., CIF Series, Vol. 9, World Scientific, Singapore, 1988, pp. 222-249.   Scanned:  pdf
  35. Olver, P.J., and Shakiban, C., Dissipative decomposition of ordinary differential equations, Proc. Roy. Soc. Edinburgh 109A (1988), 297-317.   Scanned:  pdf
  36. Olver, P.J., Generalized symmetries, in: XV International Colloquium on Group Theoretical Methods in Physics, R. Gilmore, ed., World Scientific, Singapore, 1987, pp. 216-228.   
  37. Olver, P.J., and Rosenau, P., Group-invariant solutions of differential equations, SIAM J. Appl. Math. 47 (1987), 263-278.   pdf
  38. Olver, P.J., and Rosenau, P., The construction of special solutions to partial differential equations, Phys. Lett. 114A (1986), 107-112.   pdf
  39. Olver, P.J., Noether's theorems and systems of Cauchy-Kovalevskaya type, in: Nonlinear Systems of Partial Differential Equations in Applied Mathematics, B. Nicholaenko, D.D. Holm and J.M. Hyman, eds., Lectures in Applied Math., vol. 23, part 2, Amer. Math. Soc., Providence, R.I., 1986, pp. 81-104.   
  40. Olver, P.J., Symmetry groups and path-independent integrals, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller and J.R. Willis, eds., Cambridge Univ. Press, New York, 1985, pp. 57-71.   Scanned:  pdf
  41. Olver, P.J., Symmetry groups and group invariant solutions of partial differential equations, J. Diff. Geom. 14 (1979), 497-542.   pdf
  42. Olver, P.J., and Shakiban, C., A resolution of the Euler operator I, Proc. Amer. Math. Soc. 69 (1978), 223-229.   pdf
  43. Olver, P.J., Evolution equations possessing infinitely many symmetries, J. Math. Phys. 18 (1977), 1212-1215. Reprinted in: Solitons and Particles, C. Rebbi and G. Soliani, eds., World Scientific, Singapore, 1984, pp. 235-238.   pdf

Quantum Mechanics Papers

  1. Kamran, N., Milson, R., and Olver, P.J., Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems, Adv. in Math. 156 (2000), 286-319.   pdf
  2. Olver, P.J., A quasi-exactly solvable travel guide, in: GROUP21: Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, vol. 1, H.-D. Doebner, W. Scherer, and P. Nattermann, eds., World Scientific, Singapore, 1997, pp. 285-295.   pdf
  3. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Real Lie algebras of differential operators, and quasi-exactly solvable potentials, Phil. Trans. Roy. Soc. London A 354 (1996), 1165-1193.   pdf
  4. Finkel, F., Gonzalez-Lopez, A., Kamran, N., Olver, P.J., and Rodriguez, M.A., Lie algebras of differential operators and partial integrability, in: Proceedings of IV Workshop on Differential Geometry and its Applications; Santiago de Compostela, Spain, 1995.   pdf
  5. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Quasi-exact solvability, Contemp. Math. 160 (1994), 113-140.   pdf
  6. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Quasi-exact solvability in higher dimensions, appendix in: Quasi-Exact Solvability; A.G. Ushveridze, Adam Hilger, Bristol, 1994.   
  7. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., New quasi-exactly solvable Hamiltonians in two dimensions, Commun. Math. Phys. 159 (1994), 503-537.   pdf
  8. Gonzalez-Lopez, A., Hurturbise, J., Kamran, N., and Olver, P.J., Quantification de la cohomologie des algebres de Lie de champs de vecteurs et fibres en droites sur des surfaces complexes compactes, Comptes Rendus Acad. Sci. (Paris), Serie I, 316 (1993), 1307-1312.   Scanned:  pdf
  9. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators, Commun. Math. Phys. 153 (1993), 117-146.   pdf
  10. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Lie algebras of differential operators in two complex variables, American J. Math. 114 (1992), 1163-1185.   pdf
  11. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Lie algebras of vector fields in the real plane, Proc. London Math. Soc. 64 (1992), 339-368.   pdf
  12. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., New quasi-exactly solvable Hamiltonians in two dimensions, in: Group Theoretic Methods in Physics, M.A. del Olmo, M. Santander, and J. Mateos Guilarte, eds., Proc. XIX International Colloquium, Anales de Física Monografias, Editorial Ciemat, Madrid, 1992, Vol. I, pp. 233-236.   pdf
  13. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Quasi-exactly solvable Lie algebras of first order differential operators in two complex variables, J. Phys. A 24 (1991), 3995-4008.   pdf
  14. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Lie algebras of first order differential operators in two complex variables, in: Differential Geometry, Global Analysis, and Topology, A. Nicas and W.F. Shadwick, eds., Canadian Math. Soc. Conference Proceedings, vol. 12, Amer. Math. Soc., Providence, R.I., 1991, pp. 51-84.   
  15. Kamran, N., and Olver, P.J., Lie algebras of differential operators and Lie-algebraic potentials, J. Math. Anal. Appl. 145 (1990), 342-356.   pdf
  16. Kamran, N., and Olver, P.J., Equivalence of differential operators, SIAM J. Math. Anal. 20 (1989), 1172-1185.   pdf

Fluid Mechanics and Soliton Papers

  1. Chen, G., and Olver, P.J., Numerical simulation of nonlinear dispersive quantization, Discrete Cont. Dyn. Syst. A, to appear.   pdf
  2. Chen, G., and Olver, P.J., Dispersion of discontinuous periodic waves, Proc. Roy. Soc. London A 469 (2012), 20120407.   pdf
  3. Gui, G., Liu, Y., Olver, P.J., and Qu, C., Wave-breaking and peakons for a modified Camassa-Holm equation, Commun. Math. Phys., to appear.   pdf
  4. Olver, P.J., Dispersive quantization, Amer. Math. Monthly 117 (2010), 599-610.   Corrected version: pdf   Corrections to published version: pdf
  5. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008), 344017.   Corrected version: pdf   Corrections to published version: pdf
  6. Guha, P., and Olver, P.J., Geodesic flow and two (super) component analog of the Camassa-Holm equation, SIGMA 2 (2006), 054.   pdf
  7. Foursov, M.V., Olver, P.J., and Reyes, E.G., On formal integrability of evolution equations and local geometry of surfaces, Diff. Geom. Appl., 15 (2001), 183-199.   pdf
  8. Olver, P.J., Sanders, J., and Wang, J.P., Classification of symmetry-integrable evolution equations, in: Bäcklund and Darboux Transformations. The Geometry of Solitons, A. Coley, D. Levi, R. Milson, C. Rogers and P. Winternitz, eds., CRM Proceedings & Lecture Notes, vol. 29, 2001, pp. 363-372.   pdf
  9. Foursov, M.V., and Olver, P.J., On the classification of symmetrically-coupled integrable evolution equations, in: Symmetries and Differential Equations, V.K. Andreev and Yu.V. Shanko, eds, Institute of Computational Modelling, Krasnoyarsk, Russia, 2000, pp. 244-248.   pdf
  10. Olver, P.J., and Wang, J.P., Classification of integrable one-component systems on associative algebras, Proc. London Math. Soc. 81 (2000), 566-586.   pdf
  11. Li, Y.A., and Olver, P.J., Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation, J. Diff. Eq. 162 (2000), 27-63.   pdf
  12. Li, Y.A., Olver, P.J., and Rosenau, P., Non-analytic solutions of nonlinear wave equations, in: Nonlinear Theory of Generalized Functions, M. Grosser, G. Hormann, M. Kunzinger, and M. Oberguggenberger, eds., Research Notes in Mathematics, vol. 401, Chapman and Hall/CRC, New York, 1999, pp. 129-145.   pdf
  13. Gunney, B.T.N., Li, Y.A., and Olver, P.J., Solitary waves in the critical surface tension model, J. Engin. Sci.36 (1999), 99-112.   pdf
  14. Olver, P.J., and Sokolov, V.V., Non-abelian integrable systems of the derivative nonlinear Schrödinger type, Inverse Problems 14 (1998), L5-L8.   pdf
  15. Olver, P.J., and Sokolov, V.V., Integrable evolution equations on associative algebras, Commun. Math. Phys. 193 (1998), 245-268.   pdf
  16. Li, Y.A., and Olver, P.J., Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. II. Complex analytic behavior and convergence to non-analytic solutions, Discrete Cont. Dyn. Syst. 4 (1998), 159-191.   pdf
  17. Li, Y.A., and Olver, P.J., Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. I. Compactons and peakons, Discrete Cont. Dyn. Syst. 3 (1997), 419-432.   pdf
  18. Fokas, A.S., Olver, P.J., and Rosenau, P., A plethora of integrable bi-Hamiltonian equations, in: Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman, A.S. Fokas and I.M. Gel'fand, eds., Progress in Nonlinear Differential Equations, vol. 26, Birkhäuser, Boston, 1996, pp. 93-101.   pdf
  19. Olver, P.J., and Rosenau, P., Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support, Phys. Rev. E 53 (1996), 1900-1906.   pdf
  20. Olver, P.J., Higher order models for water waves, in: Geometrical Methods in Fluid Dynamics, R. Salmon, B. Ewing-Deremer, eds., Woods Hole Oceanographic Institution, Technical Report WHOI-94-12, Woods Hole, MA, 1994, pp. 327-331.   
  21. Kichenassamy, S., and Olver, P.J., Existence and non-existence of solitary wave solutions to higher order model evolution equations, SIAM J. Math. Anal. 23 (1992), 1141-1166.   pdf
  22. Olver, P.J., Unidirectionalization of Hamiltonian waves, Phys. Lett. 126A (1988), 501-506.   pdf
  23. Clarkson, P., McLeod, J.B., Olver, P.J., and Ramani, A., Integrability of Klein-Gordon equations, SIAM J. Math. Anal. 17 (1986), 798-802.   pdf
  24. Olver, P.J., Hamiltonian perturbation theory and water waves, Contemp. Math. 28 (1984), 231-249.   Scanned:  pdf
  25. Olver, P.J., Hamiltonian and non-Hamiltonian models for water waves, in: Trends and Applications of Pure Mathematics to Mechanics, P.G. Ciarlet and M. Roseau, eds., Lecture Notes in Physics No. 195, Springer-Verlag, New York, 1984, pp. 273-290.   Scanned:  pdf
  26. Olver, P.J., Conservation laws of free boundary problems and the classification of conservation laws for water waves, Trans. Amer. Math. Soc. 277 (1983), 353-380.   pdf
  27. McLeod, J.B., and Olver, P.J., The connection between partial differential equations soluble by inverse scattering and ordinary differential equations of Painleve type, SIAM J. Math. Anal. 14 (1983), 488-506.   pdf
  28. Olver, P.J., A nonlinear Hamiltonian structure for the Euler equations, J. Math. Anal. Appl. 89 (1982), 233-250.   Spdf
  29. Benjamin, T.B., and Olver, P.J., Hamiltonian structure, symmetries and conservation laws for water waves, J. Fluid Mech. 125 (1982), 137-185.   pdf
  30. Olver, P.J., On the construction of deformations of integrable systems, preprint, University of Minnesota, 1981.   Scanned:  pdf
  31. Olver, P.J., Euler operators and conservation laws of the BBM equation, Math. Proc. Camb. Phil. Soc. 85 (1979), 143-160.   pdf
  32. Olver, P.J., Evolution equations possessing infinitely many symmetries, J. Math. Phys. 18 (1977), 1212-1215. Reprinted in: Solitons and Particles, C. Rebbi and G. Soliani, eds., World Scientific, Singapore, 1984, pp. 235-238.   pdf

Hamiltonian Papers

  1. Fernandez, O.E., Bloch, A.M., and Olver, P.J., Variational integrators for Hamiltonizable nonholonomic systems, J. Geom. Mech. 4 (2012), 137-163.   pdf
  2. Guha, P., and Olver, P.J., Geodesic flow and two (super) component analog of the Camassa-Holm equation, SIGMA 2 (2006), 054.   pdf
  3. Mari-Beffa, G., and Olver, P.J., Differential invariants for parametrized projective surfaces, Commun. Anal. Geom. 7 (1999), 807-839.   pdf
  4. Li, Y.A., and Olver, P.J., Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. II. Complex analytic behavior and convergence to non-analytic solutions, Discrete Cont. Dyn. Syst. 4 (1998), 159-191.   pdf
  5. Li, Y.A., and Olver, P.J., Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. I. Compactons and peakons, Discrete Cont. Dyn. Syst. 3 (1997), 419-432.   pdf
  6. Fokas, A.S., Olver, P.J., and Rosenau, P., A plethora of integrable bi-Hamiltonian equations, in: Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman, A.S. Fokas and I.M. Gel'fand, eds., Progress in Nonlinear Differential Equations, vol. 26, Birkhäuser, Boston, 1996, pp. 93-101.   pdf
  7. Olver, P.J., and Rosenau, P., Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support, Phys. Rev. E 53 (1996), 1900-1906.   pdf
  8. Olver, P.J., Canonical forms for biHamiltonian systems, in: The Verdier Memorial Conference on Integrable Systems, O. Babelon, P. Cartier and Y. Kosmann-Schwarzbach eds., Progress in Math., Birkhäuser, Boston, 1993, pp. 239-249.   pdf
  9. Olver, P.J., Canonical forms for compatible biHamiltonian systems, in: Solitons and Chaos, I. Antoniou and F. Lambert, eds., Springer-Verlag, New York, 1991, pp. 171-179.   
  10. Jodeit, M., and Olver, P.J., On the equation grad f = M grad g, Proc. Roy. Soc. Edinburgh 116 (1990), 341-358.   Scanned:  pdf
  11. Olver, P.J., Canonical forms and integrability of biHamiltonian systems, Phys. Lett. 148A (1990), 177-187.   pdf
  12. Kaup, D.J., and Olver, P.J., Quantization of biHamiltonian systems, J. Math. Phys. 31 (1990), 113-117.   pdf
  13. Arik, M., Neyzi, F., Nutku, Y., Olver, P.J., and Verosky, J.M., Multi-Hamiltonian structure of the Born-Infeld equation, J. Math. Phys. 30 (1989), 1338-1344.   pdf
  14. Olver, P.J., Unidirectionalization of Hamiltonian waves, Phys. Lett. 126A (1988), 501-506.   pdf
  15. Olver, P.J., and Nutku, Y., Hamiltonian structures for systems of hyperbolic conservation laws, J. Math. Phys. 29 (1988), 1610-1619.   pdf
  16. Olver, P.J., Darboux' theorem for Hamiltonian differential operators, J. Diff. Eq. 71 (1988), 10-33.   pdf
  17. Olver, P.J., Recursion operators and Hamiltonian systems, in: Symmetries and Nonlinear Phenomena, D. Levi and P. Winternitz, eds., CIF Series, Vol. 9, World Scientific, Singapore, 1988, pp. 222-249.   Scanned:  pdf
  18. Olver, P.J., BiHamiltonian systems, in: Ordinary and Partial Differential Equations, B.D. Sleeman and R.J. Jarvis, eds., Pitman Research Notes in Mathematics Series, No. 157, Longman Scientific and Technical, New York, 1987, pp. 176-193.   
  19. Olver, P.J., Dirac's theory of constraints in field theory and the canonical form of Hamiltonian differential operators, J. Math. Phys. 27 (1986), 2495-2501.   pdf
  20. Olver, P.J., Hamiltonian perturbation theory and water waves, Contemp. Math. 28 (1984), 231-249.   Scanned:  pdf
  21. Olver, P.J., Hamiltonian and non-Hamiltonian models for water waves, in: Trends and Applications of Pure Mathematics to Mechanics, P.G. Ciarlet and M. Roseau, eds., Lecture Notes in Physics No. 195, Springer-Verlag, New York, 1984, pp. 273-290.   Scanned:  pdf
  22. Olver, P.J., A nonlinear Hamiltonian structure for the Euler equations, J. Math. Anal. Appl. 89 (1982), 233-250.   pdf
  23. Benjamin, T.B., and Olver, P.J., Hamiltonian structure, symmetries and conservation laws for water waves, J. Fluid Mech. 125 (1982), 137-185.   pdf
  24. Olver, P.J., On the Hamiltonian structure of evolution equations, Math. Proc. Camb. Phil. Soc. 88 (1980), 71-88.   pdf

Elasticity Papers

  1. Bozhkov, Y., and Olver, P.J., Pohozhaev and Morawetz identities in elastostatics and elastodynamics, SIGMA 7 (2011), 055.   pdf
  2. Hatfield, G.A., and Olver, P.J., Canonical forms and conservation laws in linear elastostatics, Arch. Mech. 50 (1998), 389-404.   pdf
  3. Olver, P.J., Canonical anisotropic elastic moduli, in: Modern Theory of Anisotropic Elasticity and Applications, J.J. Wu, T.C.T. Ting and D.M. Barnett, eds., SIAM, Philadelphia, 1991, pp. 325-339.   
  4. Jodeit, M., and Olver, P.J., On the equation grad f = M grad g, Proc. Roy. Soc. Edinburgh 116 (1990), 341-358.   Scanned:  pdf
  5. Olver, P.J., and Sivaloganathan, J., The classification of null Lagrangians, Nonlinearity 1 (1988), 389-398.   pdf
  6. Olver, P.J., The equivalence problem and canonical forms for quadratic Lagrangians, Adv. Appl. Math. 9 (1988), 226-257.   pdf
  7. Olver, P.J., Conservation laws in elasticity. III. Planar linear anisotropic elastostatics, Arch. Rat. Mech. Anal. 102 (1988), 167-181.   pdf
  8. Olver, P.J., Canonical elastic moduli, J. Elasticity 19 (1988), 189-212.   pdf
  9. Olver, P.J., Conservation laws in continuum mechanics, in: Non-classical Continuum Mechanics, R.J. Knops and A.A. Lacey, eds., London Math. Soc. Lecture Note Series #122, Cambridge Univ. Press, Cambridge, 1987, pp. 96-107.   Scanned:  pdf
  10. Olver, P.J., Conservation laws and null divergences II. Nonnegative divergences, Math. Proc. Camb. Phil. Soc. 97 (1985), 511-514.   pdf
  11. Olver, P.J., Conservation laws in elasticity. II. Linear homogeneous isotropic elastostatics, Arch Rat. Mech. Anal. 85 (1984), 131-160.   pdf   Errata, Arch Rat. Mech. Anal., 102 (1988), 385-387.   pdf
  12. Olver, P.J., Symmetry groups and path-independent integrals, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller and J.R. Willis, eds., Cambridge Univ. Press, New York, 1985, pp. 57-71.   Scanned:  pdf
  13. Olver, P.J., Conservation laws in elasticity. I. General results, Arch Rat. Mech. Anal. 85 (1984), 111-129.   pdf
  14. Olver, P.J., Conservation laws and null divergences, Math. Proc. Camb. Phil. Soc. 94 (1983), 529-540.   pdf
  15. Olver, P.J., Hyperjacobians, determinantal ideals and weak solutions to variational problems, Proc. Roy. Soc. Edinburgh 95A (1983), 317-340.   Scanned:  pdf
  16. Ball, J.M., Currie, J.C., and Olver, P.J., Null Lagrangians, weak continuity, and variational problems of arbitrary order, J. Func. Anal. 41 (1981), 135-174.   pdf

Invariant Theory, Algebra, and Others

  1. Olver, P.J., Petitot, M., Solé, P., Generalized transvectants and Siegel modular forms, Adv. Appl. Math. 38 (2007), 404-418.   pdf
  2. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, H. Li, P.J. Olver, and G. Sommer, eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.   pdf
  3. Olver, P.J., Lie algebras and Lie groups, in: Encyclopedia of Nonlinear Science, A. Scott, ed., Routledge, New York, New York, 2005, pp. 526-528.   pdf
  4. Olver, P.J., Lie groups and differential equations, in: The Concise Handbook of Algebra, A.V. Mikhalev and G.F. Pilz, eds., Kluwer Acad. Publ., Dordrecht, Netherlands, 2002, pp. 92-97.   pdf
  5. Olver, P.J., Moving frames — in geometry, algebra, computer vision, and numerical analysis, in: Foundations of Computational Mathematics, R. DeVore, A. Iserles and E. Suli, eds., London Math. Soc. Lecture Note Series, vol. 284, Cambridge University Press, Cambridge, 2001, pp. 267-297.   pdf
  6. Olver, P.J., and Sanders, J., Transvectants, modular forms, and the Heisenberg algebra, Adv. Appl. Math. 25 (2000), 252-283.   pdf
  7. Berchenko, I., and Olver, P.J., Symmetries of polynomials, J. Symb. Comp. 29 (2000), 485-514.   pdf
  8. Olver, P.J., and Raphael, R., The absolute value of functions, Real Analysis Exchange, 25 (1999/2000), 257-290.   pdf
  9. Fels, M., and Olver, P.J., On relative invariants, Math. Ann. 308 (1997), 701-732.   pdf
  10. Olver, P.J., and Shakiban, C., Dissipative decomposition of partial differential equations, Rocky Mountain J. Math. 22 (1992), 1483-1510.   pdf
  11. Maliakis, M., and Olver, P.J., Explicit generalized Pieri maps, J. Algebra 148 (1992), 68-85.   pdf
  12. Olver, P.J., A nonlinear differential operator series which commutes with any function, SIAM J. Math. Anal. 23 (1992), 209-221.   pdf
  13. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians. I. Binary Forms, Adv. in Math. 80 (1990), 39-77.   pdf
  14. Olver, P.J., Invariant theory, equivalence problems and the calculus of variations, in: Invariant Theory and Tableaux, D. Stanton, ed., IMA Volumes in Mathematics and Its Applications, vol. 19, Springer-Verlag, New York, 1990, pp. 59-81.   pdf
  15. Olver, P.J., and Shakiban, C., Graph theory and classical invariant theory, Adv. in Math. 75 (1989), 212-245.   pdf
  16. Olver, P.J., and Shakiban, C., Dissipative decomposition of ordinary differential equations, Proc. Roy. Soc. Edinburgh 109A (1988), 297-317.   Scanned:  pdf
  17. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians, Bull. Amer. Math. Soc. 18 (1988), 21-26.   pdf
  18. Olver, P.J., Invariant theory and differential equations, in: Invariant Theory, S.S. Koh, ed., Lecture Notes in Mathematics, vol. 1278, Springer-Verlag, New York, 1987, pp. 62-80.   Scanned:  pdf
  19. Olver, P.J., Invariant theory of biforms, preprint, University of Minnesota, 1986.   Scanned:  pdf
  20. Olver, P.J., Hyperjacobians, determinantal ideals and weak solutions to variational problems, Proc. Roy. Soc. Edinburgh 95A (1983), 317-340.   Scanned:  pdf
  21. Olver, P.J., Differential hyperforms I, preprint, University of Minnesota, 1982.   Scanned:  pdf
  22. Olver, P.J., and Shakiban, C., A resolution of the Euler operator I, Proc. Amer. Math. Soc. 69 (1978), 223-229.   pdf