Peter Olver's Papers, Preprints, etc.

Last updated:   June 23, 2009

Moving Frames and Equivalence Papers

  1. Olver, P.J., Pohjanpelto, J., and Valiquette, F., On the structure of Lie pseudo-groups, preprint, University of Minnesota, 2009.
  2. Olver, P.J., Lectures on moving frames, preprint, University of Minnesota, 2008.
  3. Olver, P.J., Differential invariants of maximally symmetric submanifolds, J. Lie Theory 19 (2009) 79-99.
  4. Olver, P.J., Invariant variational problems and invariant flows via moving frames, preprint, University of Minnesota, 2007.
  5. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008) 344017.
  6. Olver, P.J., and Pohjanpelto, J., Differential invariant algebras of Lie pseudo-groups, Adv. in Math., to appear.
  7. Hubert, E., and Olver, P.J., Differential invariants of conformal and projective surfaces, SIGMA 3 (2007) 097.
  8. 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.
  9. Kamran, N., Olver, P.J., and Tenenblat, K., Local symplectic invariants for curves, Commun. Contemp. Math., to appear.
  10. Olver, P.J., Differential invariants of surfaces, Diff. Geom. Appl. 27 (2009) 230-239.
  11. 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.
  12. 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.
  13. 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.
  14. Olver, P.J., and Pohjanpelto, J., Moving frames for Lie pseudo-groups, Canadian J. Math. 60 (2008) 1336-1386.
  15. Olver, P.J., Generating differential invariants, J. Math. Anal. Appl. 333 (2007) 450-471.
  16. 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.
  17. Olver, P.J., and Pohjanpelto, J., Maurer-Cartan forms and the structure of Lie pseudo-groups, Selecta Math. 11 (2005) 99-126.
  18. Lewis, D., Nigam, N., and Olver, P.J., Connections for general group actions, Commun. Contemp. Math. 7 (2005) 341-374.
  19. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, Li, H., Olver, P.J., Sommer, G., eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.
  20. Olver, P.J., and Pohjanpelto, J., Regularity of pseudogroup orbits, in: Symmetry and Perturbation Theory, G. Gaeta, B. Prinari, S. Rauch-Wojciechowski, S. Terracini, eds., World Scientific, Singapore, 2005, pp. 244-254.
  21. 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.
  22. Kim, P., and Olver, P.J., Geometric integration via multi-space, Regular and Chaotic Dynamics 9 (2004) 213-226.
  23. 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.
  24. Olver, P.J., Moving frames, J. Symb. Comp. 36 (2003) 501-512.
  25. 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.
  26. Kogan, I., and Olver, P.J., Invariant Euler-Lagrange equations and the invariant variational bicomplex, Acta Appl. Math. 76 (2003) 137-193.
  27. Kogan, I., and Olver, P.J., The invariant variational bicomplex, Contemp. Math. 285 (2001) 131-144.
  28. Olver, P.J., The canonical contact form, Adv. Studies Pure Math. 37 (2002) 267-285
  29. Olver, P.J., Geometric foundations of numerical algorithms and symmetry, Appl. Alg. Engin. Comp. Commun. 11 (2001) 417-436.
  30. 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.
  31. Olver, P.J., Joint invariant signatures, Found. Comput. Math. 1 (2001) 3-67.
  32. 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 Meth. Phys., Springer-Verlag, New York, 2001, pp. 47-64.
  33. Olver, P.J., Moving frames, RIMS Kokyuroku 1150 (2000) 114-124.
  34. Olver, P.J., Moving frames and singularities of prolonged group actions, Selecta Math. 6 (2000) 41-77.
  35. Berchenko, I., and Olver, P.J., Symmetries of polynomials, J. Symb. Comp. 29 (2000) 485-514.
  36. Olver, P.J., Moving frames and joint differential invariants, Regular and Chaotic Dynamics 4 (4) (1999) 3-18.
  37. Mari-Beffa, G., and Olver, P.J., Differential invariants for parametrized projective surfaces, Commun. Anal. Geom. 7 (1999) 807-839.
  38. Fels, M., and Olver, P.J., Moving coframes. II. Regularization and theoretical foundations, Acta Appl. Math. 55 (1999) 127-208.
  39. Fels, M., Olver, P.J., Moving coframes. I. A practical algorithm, Acta Appl. Math. 51 (1998) 161-213.
  40. Fels, M., and Olver, P.J., On relative invariants, Math. Ann. 308 (1997) 701-732.
  41. Olver, P.J., Pseudo-stabilization of prolonged group actions. I. The order zero case, J. Nonlinear Math. Phys. 4 (1997) 271-277.
  42. Olver, P.J., Differential invariants, Acta Applicandae Math. 41 (1995), 271-284.
  43. Olver, P.J., Differential invariants and invariant differential equations, Lie Groups and their Appl. 1 (1994), 177-192.
  44. Olver, P.J., Equivalence and the Cartan form, Acta Applicandae Math. 31 (1993), 99-136.
  45. Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians III. New invariant differential equations, Nonlinearity 5 (1992), 601-621.
  46. Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians I. Formulation and reduction, J. Math. Pures et Appliquees 70 (1991), 369-391.
  47. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians. I. Binary Forms, Adv. in Math. 80 (1990), 39-77.
  48. 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.
  49. 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.
  50. 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.
  51. Kamran, N., and Olver, P.J., Equivalence of differential operators, SIAM J. Math. Anal. 20 (1989), 1172-1185.
  52. Kamran, N., and Olver, P.J., Equivalence problems for first order Lagrangians on the line, J. Diff. Eq. 80 (1989), 32-78.
  53. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians, Bull. Amer. Math. Soc. 18 (1988), 21-26.
  54. Olver, P.J., The equivalence problem and canonical forms for quadratic Lagrangians, Adv. Appl. Math. 9 (1988), 226-257.

Computer Vision Papers

  1. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008) 344017.
  2. 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.
  3. 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.
  4. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, Li, H., Olver, P.J., Sommer, G., eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Olver, P.J., Sapiro, G., and Tannenbaum, A., Invariant geometric evolutions of surfaces and volumetric smoothing, SIAM J. Appl. Math. 57 (1997) 176-194.
  10. Calabi, E., Olver, P.J., and Tannenbaum, A., Affine geometry, curve flows, and invariant numerical approximations, Adv. in Math. 124 (1996) 154-196.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Calabi, E., Olver, P.J., and Tannenbaum, A., Invariant numerical approximations to differential invariant signatures, preprint, University of Minnesota, 1995.
  16. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P., and Tannenbaum, A., A gradient surface evolution approach to 3D segmentation, in: Proceedings of IS&T, Minneapolis, MN, 1995
  17. 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.
  18. 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, the Netherlands, 1994, pp. 255-306.
  19. 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.

Numerical Analysis Papers

  1. 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.
  2. Olver, P.J., On multivariate interpolation, Stud. Appl. Math. 116 (2006) 201-240.
  3. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, Li, H., Olver, P.J., Sommer, G., eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.
  4. Lewis, D., Nigam, N., and Olver, P.J., Connections for general group actions, Commun. Contemp. Math. 7 (2005) 341-374.
  5. Kim, P., and Olver, P.J., Geometric integration via multi-space, Regular and Chaotic Dynamics 9 (2004) 213-226.
  6. Lewis, D., and Olver, P.J., Geometric integration algorithms on homogeneous manifolds, Found. Comput. Math. 3 (2002) 363-392.
  7. Olver, P.J., Geometric foundations of numerical algorithms and symmetry, Appl. Alg. Engin. Comp. Commun. 11 (2001) 417-436.
  8. 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.
  9. 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.
  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.
  11. Calabi, E., Olver, P.J., and Tannenbaum, A., Affine geometry, curve flows, and invariant numerical approximations, Adv. in Math. 124 (1996) 154-196.

Symmetry Papers

  1. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008) 344017.
  2. 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.
  3. Muriel, C., Romero, J.L., and Olver, P.J., Variational C∞ symmetries and Euler-Lagrange equations, J. Diff. Eq. 222 (2006) 164-184.
  4. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, Li, H., Olver, P.J., Sommer, G., eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.
  5. 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.
  6. 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.
  7. 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.
  8. Kogan, I., and Olver, P.J., Invariant Euler-Lagrange equations and the invariant variational bicomplex, Acta Appl. Math. 76 (2003) 137-193.
  9. 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.
  10. Olver, P.J., Sanders, J., and Wang, J.P., Ghost symmetries, J. Nonlinear Math. Phys. 9, Suppl. 1 (2002) 164-172.
  11. Kogan, I., and Olver, P.J., The invariant variational bicomplex, Contemp. Math. 285 (2001) 131-144.
  12. 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.
  13. Olver, P.J., Geometric foundations of numerical algorithms and symmetry, Appl. Alg. Engin. Comp. Commun. 11 (2001) 417-436.
  14. Olver, P.J., Sanders, J., and Wang, J.P., Classification of symmetry-integrable evolution equations, CRM Proc. Lecture Notes, 29 (2001) 363-372.
  15. 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.
  16. Olver, P.J., and Wang, J.P., Classification of integrable one-component systems on associative algebras, Proc. London Math. Soc. 81 (2000) 566-586.
  17. 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.
  18. Olver, P.J., and Sokolov, V.V., Non-abelian integrable systems of the derivative nonlinear Schrödinger type, Inverse Problems 14 (1998) L5-L8.
  19. Olver, P.J., and Sokolov, V.V., Integrable evolution equations on associative algebras, Commun. Math. Phys. 193 (1998) 245-268.
  20. 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.
  21. Heredero, R.H., and Olver, P.J., Classification of invariant wave equations, J. Math. Phys. 37 (1996) 6414-6438.
  22. Olver, P.J., Non-associative local Lie groups, J. Lie Theory 6 (1996) 23-51.
  23. Clarkson, P.A., and Olver, P.J., Symmetry and the Chazy equation, J. Diff. Eq. 124 (1996), 225-246.
  24. 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.
  25. Olver, P.J., Differential invariants, Acta Applicandae Math. 41 (1995), 271-284.
  26. Olver, P.J., Differential invariants and invariant differential equations, Lie Groups and their Appl. 1 (1994), 177-192.
  27. Olver, P.J., Direct reduction and differential constraints, Proc. Roy. Soc. London A 444 (1994), 509-523.
  28. Anderson, I.M., Kamran, N., and Olver, P.J., Internal, external and generalized symmetries, Adv. in Math. 100 (1993), 53-100.
  29. 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, The Netherlands, 1993, pp. 7-21.
  30. Olver, P.J., and Shakiban, C., Dissipative decomposition of partial differential equations, Rocky Mountain J. Math. 22 (1992), 1483-1510.
  31. Olver, P.J., Symmetry and explicit solutions of partial differential equations, Appl. Numerical Math. 10 (1992), 307-324.
  32. 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.
  33. 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.
  34. Olver, P.J., and Shakiban, C., Dissipative decomposition of ordinary differential equations, Proc. Roy. Soc. Edinburgh 109A (1988), 297-317.
  35. 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.
  36. Olver, P.J., and Rosenau, P., Group-invariant solutions of differential equations, SIAM J. Appl. Math. 47 (1987), 263-278.
  37. Olver, P.J., and Rosenau, P., The construction of special solutions to partial differential equations, Phys. Lett. 114A (1986), 107-112.
  38. 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.
  39. 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.
  40. Olver, P.J., Symmetry groups and group invariant solutions of partial differential equations, J. Diff. Geom. 14 (1979), 497-542.
  41. Olver, P.J., and Shakiban, C., A resolution of the Euler operator I, Proc. Amer. Math. Soc. 69 (1978), 223-229.
  42. 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

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.
  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, P. Nattermann, eds., World Scientific, Singapore, 1997, pp. 285-295.
  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.
  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.
  5. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Quasi-exact solvability, Contemp. Math. 160 (1994), 113-140.
  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.
  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.
  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.
  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.
  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.
  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.
  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.
  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.
  16. Kamran, N., and Olver, P.J., Equivalence of differential operators, SIAM J. Math. Anal. 20 (1989), 1172-1185.

Fluid Mechanics and Soliton Papers

  1. Olver, P.J., Dispersive quantization, preprint, University of Minnesota, 2009.
  2. Olver, P.J., Invariant submanifold flows, J. Phys. A 41 (2008) 344017.
  3. Guha, P., and Olver, P.J., Geodesic flow and two (super) component analog of the Camassa-Holm equation, SIGMA 2 (2006) 054.
  4. 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.
  5. Olver, P.J., Sanders, J., and Wang, J.P., Classification of symmetry-integrable evolution equations, CRM Proc. Lecture Notes, 29 (2001) 363-372.
  6. 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.
  7. Olver, P.J., and Wang, J.P., Classification of integrable one-component systems on associative algebras, Proc. London Math. Soc. 81 (2000) 566-586.
  8. 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.
  9. 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.
  10. 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.
  11. Olver, P.J., and Sokolov, V.V., Non-abelian integrable systems of the derivative nonlinear Schrödinger type, Inverse Problems 14 (1998) L5-L8.
  12. Olver, P.J., and Sokolov, V.V., Integrable evolution equations on associative algebras, Commun. Math. Phys. 193 (1998) 245-268.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. Olver, P.J., Unidirectionalization of Hamiltonian waves, Phys. Lett. 126A (1988), 501-506.
  20. Clarkson, P., McLeod, J.B., Olver, P.J., and Ramani, A., Integrability of Klein-Gordon equations, SIAM J. Math. Anal. 17 (1986), 798-802.
  21. Olver, P.J., Hamiltonian perturbation theory and water waves, Contemp. Math. 28 (1984), 231-249.
  22. 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.
  23. 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.
  24. 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.
  25. Olver, P.J., A nonlinear Hamiltonian structure for the Euler equations, J. Math. Anal. Appl. 89 (1982), 233-250.
  26. Benjamin, T.B., and Olver, P.J., Hamiltonian structure, symmetries and conservation laws for water waves, J. Fluid Mech. 125 (1982), 137-185.
  27. Olver, P.J., Euler operators and conservation laws of the BBM equation, Math. Proc. Camb. Phil. Soc. 85 (1979), 143-160.
  28. 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

Hamiltonian Papers

  1. Guha, P., and Olver, P.J., Geodesic flow and two (super) component analog of the Camassa-Holm equation, SIGMA 2 (2006) 054.
  2. Mari-Beffa, G., and Olver, P.J., Differential invariants for parametrized projective surfaces, Commun. Anal. Geom. 7 (1999) 807-839.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Jodeit, M., and Olver, P.J., On the equation grad f = M grad g, Proc. Roy. Soc. Edinburgh 116 (1990), 341-358.
  10. Olver, P.J., Canonical forms and integrability of biHamiltonian systems, Phys. Lett. 148A (1990), 177-187.
  11. Kaup, D.J., and Olver, P.J., Quantization of biHamiltonian systems, J. Math. Phys. 31 (1990), 113-117.
  12. 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.
  13. Olver, P.J., Unidirectionalization of Hamiltonian waves, Phys. Lett. 126A (1988), 501-506.
  14. Olver, P.J., and Nutku, Y., Hamiltonian structures for systems of hyperbolic conservation laws, J. Math. Phys. 29 (1988), 1610-1619.
  15. Olver, P.J., Darboux' theorem for Hamiltonian differential operators, J. Diff. Eq. 71 (1988), 10-33.
  16. 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.
  17. 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.
  18. 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.
  19. Olver, P.J., Hamiltonian perturbation theory and water waves, Contemp. Math. 28 (1984), 231-249.
  20. 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.
  21. Olver, P.J., A nonlinear Hamiltonian structure for the Euler equations, J. Math. Anal. Appl. 89 (1982), 233-250.
  22. Benjamin, T.B., and Olver, P.J., Hamiltonian structure, symmetries and conservation laws for water waves, J. Fluid Mech. 125 (1982), 137-185.
  23. Olver, P.J., On the Hamiltonian structure of evolution equations, Math. Proc. Camb. Phil. Soc. 88 (1980), 71-88.

Elasticity Papers

  1. Hatfield, G.A., and Olver, P.J., Canonical forms and conservation laws in linear elastostatics, Arch. Mech. 50 (1998) 389-404.
  2. 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.
  3. Jodeit, M., and Olver, P.J., On the equation grad f = M grad g, Proc. Roy. Soc. Edinburgh 116 (1990), 341-358.
  4. Olver, P.J., and Sivaloganathan, J., The classification of null Lagrangians, Nonlinearity 1 (1988), 389-398.
  5. Olver, P.J., The equivalence problem and canonical forms for quadratic Lagrangians, Adv. Appl. Math. 9 (1988), 226-257.
  6. Olver, P.J., Conservation laws in elasticity. III. Planar linear anisotropic elastostatics, Arch. Rat. Mech. Anal. 102 (1988), 167-181.
  7. Olver, P.J., Canonical elastic moduli, J. Elasticity 19 (1988), 189-212.
  8. 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.
  9. Olver, P.J., Conservation laws and null divergences II. Nonnegative divergences, Math. Proc. Camb. Phil. Soc. 97 (1985), 511-514.
  10. Olver, P.J., Conservation laws in elasticity. II. Linear homogeneous isotropic elastostatics, Arch Rat. Mech. Anal. 85 (1984), 131-160; also: Errata, Arch Rat. Mech. Anal., 102 (1988), 385-387.
  11. 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.
  12. Olver, P.J., Conservation laws in elasticity. I. General results, Arch Rat. Mech. Anal. 85 (1984), 111-129.
  13. Olver, P.J., Conservation laws and null divergences, Math. Proc. Camb. Phil. Soc. 94 (1983), 529-540.
  14. Olver, P.J., Hyperjacobians, determinantal ideals and weak solutions to variational problems, Proc. Roy. Soc. Edinburgh 95A (1983), 317-340.
  15. 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.

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.
  2. Olver, P.J., A survey of moving frames, in: Computer Algebra and Geometric Algebra with Applications, Li, H., Olver, P.J., Sommer, G., eds., Lecture Notes in Computer Science, vol. 3519, Springer-Verlag, New York, 2005, pp. 105-138.
  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.
  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.
  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.
  6. Olver, P.J., and Sanders, J., Transvectants, modular forms, and the Heisenberg algebra, Adv. Appl. Math. 25 (2000) 252-283.
  7. Berchenko, I., and Olver, P.J., Symmetries of polynomials, J. Symb. Comp. 29 (2000) 485-514.
  8. Olver, P.J., and Raphael, R., The absolute value of functions, Real Analysis Exchange, 25 (1999/2000) 257-290.
  9. Fels, M., and Olver, P.J., On relative invariants, Math. Ann. 308 (1997) 701-732.
  10. Olver, P.J., and Shakiban, C., Dissipative decomposition of partial differential equations, Rocky Mountain J. Math. 22 (1992), 1483-1510.
  11. Maliakis, M., and Olver, P.J., Explicit generalized Pieri maps, J. Algebra 148 (1992), 68-85.
  12. Olver, P.J., A nonlinear differential operator series which commutes with any function, SIAM J. Math. Anal. 23 (1992), 209-221.
  13. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians. I. Binary Forms, Adv. in Math. 80 (1990), 39-77.
  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.
  15. Olver, P.J., and Shakiban, C., Graph theory and classical invariant theory, Adv. in Math. 75 (1989), 212-245.
  16. Olver, P.J., and Shakiban, C., Dissipative decomposition of ordinary differential equations, Proc. Roy. Soc. Edinburgh 109A (1988), 297-317.
  17. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians, Bull. Amer. Math. Soc. 18 (1988), 21-26.
  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.
  19. Olver, P.J., Invariant theory of biforms, preprint, 1986.
  20. Olver, P.J., Hyperjacobians, determinantal ideals and weak solutions to variational problems, Proc. Roy. Soc. Edinburgh 95A (1983), 317-340.
  21. Olver, P.J., Differential hyperforms I, preprint, 1982.
  22. Olver, P.J., and Shakiban, C., A resolution of the Euler operator I, Proc. Amer. Math. Soc. 69 (1978), 223-229.