Peter Olver's Published Papers

Last updated:   June 17, 2008
  1. Olver, P.J., Differential invariants of surfaces, Diff. Geom. Appl., to appear.
  2. Olver, P.J., Invariant submanifold flows, J. Phys. A, to appear.
  3. Cheh, J., Olver, P.J., and Pohjanpelto, J., Algorithms for differential invariants of symmetry groups of differential equations, Found. Comput. Math., to appear.
  4. Olver, P.J., and Pohjanpelto, J., Moving frames for Lie pseudo-groups, Canadian J. Math., to appear.
  5. Hubert, E., and Olver, P.J., Differential invariants of conformal and projective surfaces, SIGMA 3 (2007) 097; arXiv:0710.0519.
  6. Olver, P.J., Generating differential invariants, J. Math. Anal. Appl. 333 (2007) 450-471.
  7. Olver, P.J., Petitot, M., Solé, P., Generalized transvectants and Siegel modular forms, Adv. Appl. Math. 38 (2007) 404-418.
  8. Guha, P., and Olver, P.J., Geodesic flow and two (super) component analog of the Camassa-Holm equation, SIGMA 2 (2006) 054.
  9. Muriel, C., Romero, J.L., and Olver, P.J., Variational C∞ symmetries and Euler-Lagrange equations, J. Diff. Eq. 222 (2006) 164-184.
  10. Olver, P.J., On multivariate interpolation, Stud. Appl. Math. 116 (2006) 201-240.
  11. Lewis, D., Nigam, N., and Olver, P.J., Connections for general group actions, Commun. Contemp. Math. 7 (2005) 341-374.
  12. Olver, P.J., and Pohjanpelto, J., Maurer-Cartan forms and the structure of Lie pseudo-groups, Selecta Math. 11 (2005) 99-126.
  13. 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.
  14. Kim, P., and Olver, P.J., Geometric integration via multi-space, Regular and Chaotic Dynamics 9 (2004) 213-226.
  15. Olver, P.J., Moving frames, J. Symb. Comp. 36 (2003) 501-512.
  16. Kogan, I., and Olver, P.J., Invariant Euler-Lagrange equations and the invariant variational bicomplex, Acta Appl. Math. 76 (2003) 137-193.
  17. Olver, P.J., The canonical contact form, Adv. Studies Pure Math. 37 (2002) 267-285
  18. Lewis, D., and Olver, P.J., Geometric integration algorithms on homogeneous manifolds, Found. Comput. Math. 3 (2002) 363-392.
  19. Olver, P.J., Sanders, J., and Wang, J.P., Ghost symmetries, J. Nonlinear Math. Phys. 9, Suppl. 1 (2002) 164-172.
  20. Kogan, I., and Olver, P.J., The invariant variational bicomplex, Contemp. Math. 285 (2001) 131-144.
  21. 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.
  22. Olver, P.J., Geometric foundations of numerical algorithms and symmetry, Appl. Alg. Engin. Comp. Commun. 11 (2001) 417-436.
  23. Olver, P.J., Joint invariant signatures, Found. Comput. Math. 1 (2001) 3-67.
  24. 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.
  25. Olver, P.J., and Wang, J.P., Classification of integrable one-component systems on associative algebras, Proc. London Math. Soc. 81 (2000) 566-586.
  26. Olver, P.J., and Sanders, J., Transvectants, modular forms, and the Heisenberg algebra, Adv. Appl. Math. 25 (2000) 252-283.
  27. Berchenko, I., and Olver, P.J., Symmetries of polynomials, J. Symb. Comp. 29 (2000) 485-514.
  28. Olver, P.J., Moving frames and singularities of prolonged group actions, Selecta Math. 6 (2000) 41-77.
  29. 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.
  30. Olver, P.J., and Raphael, R., The absolute value of functions, Real Analysis Exchange, 25 (1999/2000) 257-290.
  31. Olver, P.J., Moving frames and joint differential invariants, Regular and Chaotic Dynamics 4 (4) (1999) 3-18.
  32. 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.
  33. Mari-Beffa, G., and Olver, P.J., Differential invariants for parametrized projective surfaces, Commun. Anal. Geom. 7 (1999) 807-839.
  34. 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.
  35. Fels, M., and Olver, P.J., Moving coframes. II. Regularization and theoretical foundations, Acta Appl. Math. 55 (1999) 127-208.
  36. Olver, P.J., and Sokolov, V.V., Non-abelian integrable systems of the derivative nonlinear Schrödinger type, Inverse Problems 14 (1998) L5-L8.
  37. Hatfield, G.A., and Olver, P.J., Canonical forms and conservation laws in linear elastostatics, Arch. Mech. 50 (1998) 389-404.
  38. Fels, M., Olver, P.J., Moving coframes. I. A practical algorithm, Acta Appl. Math. 51 (1998) 161-213.
  39. Olver, P.J., and Sokolov, V.V., Integrable evolution equations on associative algebras, Commun. Math. Phys. 193 (1998) 245-268.
  40. 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.
  41. 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.
  42. Fels, M., and Olver, P.J., On relative invariants, Math. Ann. 308 (1997) 701-732.
  43. 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.
  44. Olver, P.J., Pseudo-stabilization of prolonged group actions. I. The order zero case, J. Nonlinear Math. Phys. 4 (1997) 271-277.
  45. 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.
  46. Olver, P.J., Sapiro, G., and Tannenbaum, A., Invariant geometric evolutions of surfaces and volumetric smoothing, SIAM J. Appl. Math. 57 (1997) 176-194.
  47. Calabi, E., Olver, P.J., and Tannenbaum, A., Affine geometry, curve flows, and invariant numerical approximations, Adv. in Math. 124 (1996) 154-196.
  48. Heredero, R.H., and Olver, P.J., Classification of invariant wave equations, J. Math. Phys. 37 (1996) 6414-6438.
  49. 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.
  50. Olver, P.J., Non-associative local Lie groups, J. Lie Theory 6 (1996) 23-51.
  51. 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.
  52. 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.
  53. Clarkson, P.A., and Olver, P.J., Symmetry and the Chazy equation, J. Diff. Eq. 124 (1996), 225-246.
  54. Olver, P.J., Differential invariants, Acta Applicandae Math. 41 (1995), 271-284.
  55. Olver, P.J., Differential invariants and invariant differential equations, Lie Groups and their Appl. 1 (1994), 177-192.
  56. 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.
  57. Olver, P.J., Direct reduction and differential constraints, Proc. Roy. Soc. London A 444 (1994), 509-523.
  58. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., Quasi-exact solvability, Contemp. Math. 160 (1994), 113-140.
  59. Gonzalez-Lopez, A., Kamran, N., and Olver, P.J., New quasi-exactly solvable Hamiltonians in two dimensions, Commun. Math. Phys. 159 (1994), 503-537.
  60. Anderson, I.M., Kamran, N., and Olver, P.J., Internal, external and generalized symmetries, Adv. in Math. 100 (1993), 53-100.
  61. 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.
  62. Olver, P.J., Equivalence and the Cartan form, Acta Applicandae Math. 31 (1993), 99-136.
  63. 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.
  64. Olver, P.J., and Shakiban, C., Dissipative decomposition of partial differential equations, Rocky Mountain J. Math. 22 (1992), 1483-1510.
  65. 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.
  66. Olver, P.J., Symmetry and explicit solutions of partial differential equations, Appl. Numerical Math. 10 (1992), 307-324.
  67. 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.
  68. Maliakis, M., and Olver, P.J., Explicit generalized Pieri maps, J. Algebra 148 (1992), 68-85.
  69. 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.
  70. Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians III. New invariant differential equations, Nonlinearity 5 (1992), 601-621.
  71. Olver, P.J., A nonlinear differential operator series which commutes with any function, SIAM J. Math. Anal. 23 (1992), 209-221.
  72. 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.
  73. Kamran, N., and Olver, P.J., Equivalence of higher order Lagrangians I. Formulation and reduction, J. Math. Pures et Appliquees 70 (1991), 369-391.
  74. Jodeit, M., and Olver, P.J., On the equation grad f = M grad g, Proc. Roy. Soc. Edinburgh 116 (1990), 341-358.
  75. Olver, P.J., Canonical forms and integrability of biHamiltonian systems, Phys. Lett. 148A (1990), 177-187.
  76. Kaup, D.J., and Olver, P.J., Quantization of biHamiltonian systems, J. Math. Phys. 31 (1990), 113-117.
  77. Kamran, N., and Olver, P.J., Lie algebras of differential operators and Lie-algebraic potentials, J. Math. Anal. Appl. 145 (1990), 342-356.
  78. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians. I. Binary Forms, Adv. in Math. 80 (1990), 39-77.
  79. 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.
  80. 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.
  81. 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.
  82. Kamran, N., and Olver, P.J., Equivalence of differential operators, SIAM J. Math. Anal. 20 (1989), 1172-1185.
  83. Kamran, N., and Olver, P.J., Equivalence problems for first order Lagrangians on the line, J. Diff. Eq. 80 (1989), 32-78.
  84. Olver, P.J., and Shakiban, C., Graph theory and classical invariant theory, Adv. in Math. 75 (1989), 212-245.
  85. Olver, P.J., and Nutku, Y., Hamiltonian structures for systems of hyperbolic conservation laws, J. Math. Phys. 29 (1988), 1610-1619.
  86. Olver, P.J., and Shakiban, C., Dissipative decomposition of ordinary differential equations, Proc. Roy. Soc. Edinburgh 109A (1988), 297-317.
  87. Olver, P.J., Unidirectionalization of Hamiltonian waves, Phys. Lett. 126A (1988), 501-506.
  88. Olver, P.J., and Sivaloganathan, J., The classification of null Lagrangians, Nonlinearity 1 (1988), 389-398.
  89. Olver, P.J., Classical invariant theory and the equivalence problem for particle Lagrangians, Bull. Amer. Math. Soc. 18 (1988), 21-26.
  90. Olver, P.J., Conservation laws in elasticity. III. Planar linear anisotropic elastostatics, Arch. Rat. Mech. Anal. 102 (1988), 167-181.
  91. Olver, P.J., Canonical elastic moduli, J. Elasticity 19 (1988), 189-212.
  92. Olver, P.J., The equivalence problem and canonical forms for quadratic Lagrangians, Adv. Appl. Math. 9 (1988), 226-257.
  93. Olver, P.J., Darboux' theorem for Hamiltonian differential operators, J. Diff. Eq. 71 (1988), 10-33.
  94. Olver, P.J., and Rosenau, P., Group-invariant solutions of differential equations, SIAM J. Appl. Math. 47 (1987), 263-278.
  95. 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.
  96. Olver, P.J., and Rosenau, P., The construction of special solutions to partial differential equations, Phys. Lett. 114A (1986), 107-112.
  97. Clarkson, P., McLeod, J.B., Olver, P.J., and Ramani, A., Integrability of Klein-Gordon equations, SIAM J. Math. Anal. 17 (1986), 798-802.
  98. Olver, P.J., Conservation laws and null divergences II. Nonnegative divergences, Math. Proc. Camb. Phil. Soc. 97 (1985), 511-514.
  99. Olver, P.J., Hamiltonian perturbation theory and water waves, Contemp. Math. 28 (1984), 231-249.
  100. 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.
  101. Olver, P.J., Conservation laws in elasticity. I. General results, Arch Rat. Mech. Anal. 85 (1984), 111-129.
  102. Olver, P.J., Conservation laws and null divergences, Math. Proc. Camb. Phil. Soc. 94 (1983), 529-540.
  103. Olver, P.J., Hyperjacobians, determinantal ideals and weak solutions to variational problems, Proc. Roy. Soc. Edinburgh 95A (1983), 317-340.
  104. 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.
  105. 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.
  106. Olver, P.J., A nonlinear Hamiltonian structure for the Euler equations, J. Math. Anal. Appl. 89 (1982), 233-250.
  107. Benjamin, T.B., and Olver, P.J., Hamiltonian structure, symmetries and conservation laws for water waves, J. Fluid Mech. 125 (1982), 137-185.
  108. 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.
  109. Olver, P.J., On the Hamiltonian structure of evolution equations, Math. Proc. Camb. Phil. Soc. 88 (1980), 71-88.
  110. Olver, P.J., Euler operators and conservation laws of the BBM equation, Math. Proc. Camb. Phil. Soc. 85 (1979), 143-160.
  111. Olver, P.J., Symmetry groups and group invariant solutions of partial differential equations, J. Diff. Geom. 14 (1979), 497-542.
  112. Olver, P.J., and Shakiban, C., A resolution of the Euler operator I, Proc. Amer. Math. Soc. 69 (1978), 223-229.
  113. 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