C e n t r e  d e  r e c h e r c h e s  m a t h é m a t i q u e s

P. Winternitz

Articles (published or accepted)

  1. D. Levi and P. Winternitz. Continuous symmetries of difference equations. J. Phys. A, 39(2), R1-R63, 2006. [nlin.SI/0502004]
  2. F. Valiquette and P. Winternitz. Discretization of partial differential equations preserving their physical symmetries. J. Phys. A 38(45) 9765-9783, 2005. [math-ph/0507061]
  3. E.G. Kalnins, Z. Thomova, and P. Winternitz. Subgroup type coordinates in four-dimensional flat spaces. J. Nonl. Math. Phys. 12 (2): 35-64, 2005. [math-ph/0405063]
  4. L. Snobl and P. Winternitz. A class of solvable Lie algebras and their Casimir invariants. J. Phys. A 38 (12): 2687-2700, 2005.
  5. F. Gungor and P. Winternitz. Equivalence classes and symmetries of the variable coefficient Kadomtsev-Petviashvili equation. Nonlinear Dynamics 35 (4): 381-396, 2004.
  6. D. Levi, P. Tempesta and P. Winternitz. Umbral calculus, difference equations and the discrete Schroedinger equation. J. Math. Phys., 45 (11): 4077-4105, 2004.
  7. M. A. Rodriguez and P. Winternitz. Lie symmetries and exact solutions of first order difference schemes . J. Phys. A 37 (23): 6129-6142, 2004.
  8. A. V. Penskoi and P. Winternitz. Discrete Riccati equations with superposition formulas . J. Math. Anal. Appl. 294 (2): 533-547, 2004.
  9. J. Bérubé and P. Winternitz. Integrable and superintegrable systems in a magnetic field. J.Math.Phys., 45 (5):1959-1973, 2004.
  10. D. Levi, P. Tempesta and P. Winternitz. Lorentz and Galilei invariance on lattices. Phys. Rev. D., 69 (10):105011,1-6, 2004.
  11. V. Dorodnitsyn, R. Kozlov, and P. Winternitz. Continuous symmetries of Lagrangians and exact solutions of discrete equations. J.Math.Phys., 45(1):336-359, 2004.
  12. E.G. Kalnins, J. M. Kress, W. Jr. Miller, and P. Winternitz. Superintegrable systems in Darboux spaces. J.Math.Phys., 44(12): 5811-5848, 2003.
  13. V. Dorodnitsyn, R. Kozlov, and P. Winternitz. Symmetries, Lagrangian formalism and integration of second order difference equations . J. Nonlinear Math. Phys. 10, Suppl. 2: 41-56, 2003.
  14. M.A. Grundland, P.Tempesta, and P.Winternitz. Weak transversality and partially invariant solutions. J.Math.Phys., 44(6):2704-2722, 2003.
  15. G. Pogosyan, A.Sissakian, and P.Winternitz. Separation of variables and Lie algebra contractions. Applications to special functions. Phys. Elem. Part. Nucl., 33(7), 235-276, 2002.
  16. S. Gravel and P. Winternitz. Superintegrability with third order integrals in quantum and classical mechanics. J. Math. Phys. , 43 (12), 5902 - 5912, 2002.
  17. G.S. Pogosyan and P. Winternitz. Separation of variables and subgroup bases on n-dimensional hyperboloids. J.Math.Phys. , 43(6), 3387-3410, 2002.
  18. D. Levi and P. Winternitz. Lie point symmetries and commuting flows for equations on lattices. J.Phys.A., 35(9):2249-2262, 2002.
  19. M.A. Rodriguez and P.Winternitz. Quantum superintegrability and exact solvability in n dimensions. J.Math.Phys., 43(3):1309-1322, 2002.
  20. E.G. Kalnins, J. Kress, and P.Winternitz. Superintegrability in a two-dimensional space of nonconstant curvature. J.Math Phys. , 43(2):970-983, 2002.
  21. D. Levi, S. Tremblay, and P.Winternitz. Lie symmetries of multidimensional difference equations. J.Phys.A., 34(44):9507-9524, 2001.
  22. L. Martina, M.B. Sheftel, and Winternitz P. Group foliation and noninvariant solutions of the heavenly equations. J.Phys.A. , 34(43):9243-9263, 2001.
  23. S. Tremblay and P. Winternitz. Invariants of nilpotent and solvable triangular Lie algebras. J.Phys.A, 34(42):9085-9099, 2001.
  24. S. Lafortune, S. Tremblay, and P. Winternitz. Symmetry classification of diatomic molecular chains. J.Math.Phys. , 42(11):5341-5357, 2001.
  25. R. Hernandez Heredero, D. Levi, and P. Winternitz. Symmetries of the discrete nonlinear Schroedinger equation. Theor.Math.Phys ., 127(3):729-737, 2001.
  26. P. Tempesta, A.V. Turbiner, and P. Wintrnitz. Exact solvability of superintegrable systems. J.Math.Phys., 42 (9), 4248-4257, 2001.
  27. D. Levi, S. Tremblay, and P. Winternitz. Continuous symmetries of equations on lattices. Czech J.Phys. , 51(46):349-356, 2001.
  28. M.B. Sheftel, P. Tempesta, and P. Winternitz. Recursion operators, higher order symmetries and superintegrability in quantum mechanics. . Czech. J. Phys., 51(4):392-399, 2001.
  29. M.B. Sheftel, P. Tempesta, and P. Winternitz. Superintegrable systems in quantum mechanics and classical Lie theory. J. Math. Phys. , 42(2):659-673, 2001.
  30. R. Hernandez-Heredero, D. Levi, and P. Winternitz. Relation between Backlund transformations and higher continuous symmetries of the Toda equation. J.Phys.A , 34(11):2459-2465, 2001.
  31. A.A. Izmestiev, G.S. Pogosyan, A.N. Sissakian, and P. Winternitz. Contractions of Lie algebras and the separation of variables: interbase expansions. J.Phys.A., 34(3):521-554, 2001.
  32. D. Levi, S. Tremblay, and P. Winternitz. Lie point symmetries of difference equations and lattices. J.Phys.A , 33(46):8507-8524, 2000.
  33. A. Grundland, M. Sheftel, and P. Winternitz. Invariant solutions of equations of the hydrodynamic type. J.Phys.A , 33(46):8193-8215, 2000.
  34. L. Martina, S. Lafortune, and P. Winternitz. Point symmetries of generalized Toda field theories ii. Symmetry reduction. . J.Phys.A, 33(36):6431-6446, 2000.
  35. N. Atakishiyev and P. Winternitz. Bases for representations of quantum algebras. J.Phys.A, 33(30):5303-5313, 2000.
  36. R. Hernandez-Heredero, D. Levi, M. Rodriguez, and P. Winternitz. Lie algebra contractions and symmetries of the Toda hierarchy . J.Phys.A, 33(28):5025-5040, 2000.
  37. V. Dorodnitsyn and P. Winternitz. Lie point symmetry preserving discretizations for variable coefficient Korteweg-de Vries equations . Nonlinear Dynamics, 22(1):49-59, 2000.
  38. S. Lafortune, L. Martina, and P. Winternitz. Point symmetries of generalized Toda field theories. J.Phys.A , 33:2419-2435, 2000.
  39. E. McSween and P. Winternitz. Integrable and superintegrable Hamiltonian systems in magnetic fields. J.Math.Phys, 41(5):2957-2967, 2000.
  40. Y. Y. Berest and P. Winternitz. Huygens' principle and separation of variables. Int. J. Math. Phys., 12(2):159-180, 2000.
  41. V. Dorodnitsyn, R. Kozlov, and P. Winternitz. Lie group classification of second order difference equations. J.Math. Phys., 41(1):480-504, 2000.
  42. A. Ankiewicz, A. Akhmediev, and P. Winternitz. Singularity analysis, balance equations and soliton solution of nonlocal complex Ginzburg Landau equation. J.Engin.Math., 36(1):11-24, 1999.
  43. Z. Thomova and P. Winternitz. Maximal abelian subalgebras of pseudoeuclidean Lie algebras. Lin. Alg. Appl., 291:245-274, 1999.
  44. D. Gomez-Ullate, S. Lafortune, and P. Winternitz. Symmetries of discrete dynamical systems involving two species. J.Math.Phys., 40(6):2782-2804, 1999.
  45. M. Havlicek, M. Posta, and P. Winternitz. Nonlinear superposition formulas based on imprimitive group action. J.Math.Phys. , 40(6):3104-3122, 1999.
  46. M. A. Ayari, V. Hussin, and P. Winternitz. Group invariant solutions for the super Korteweg-de Vries equation (N=2). J.Math.Phys. , 40(4):1951-1965, 1999.
  47. R. Hernandez Heredero, D. Levi, and P. Winternitz. Symmetries of the discrete Burgers equation. J.Phys.A, 32(14):2685-2695, 1999.
  48. J. Patera, G. Pogosyan, and P. Winternitz. Graded contractions of the Lie algebra e(2,1). J. Phys. A, 32:805-826, 1999.
  49. A. Izmest'ev, G. S. Pogosyan, A. Sissakian, and P. Winternitz. Contractions of Lie algebras and separation of variables. The n-dimensional sphere. J. Math. Phys, 40(3):1549-1573, 1999.
  50. S. Lafortune, C. Menyuk, and P. Winternitz. Solutions to the optical cascading equations. Phys. Rev. E, 58(2):2518-2525, 1998.
  51. Z. Thomova, P. Winternitz, and W. Zakrzewski. Solutions of (2+1)-dimensional spin systems. J. Math. Phys., 39(7):3927-3944, 1998.
  52. Z. Thomova and P. Winternitz. Maximal Abelian subgroups of the isometry and conformal groups of Euclidean and Minkowski spaces . J. Phys. A, 31:1831-1858, 1998.
  53. S. Tremblay and P. Winternitz. Solvable Lie algebras with triangular nilradicals. J. Phys. A, 31:789-806, 1998. .
  54. C. Rogers, W. Schief, and P. Winternitz. Lie theoretical generalization and discretization of the Pinney equation. J. Math. Anal. Appl., 216:246-264, 1997.
  55. Y. A. Orlov and P. Winternitz. $P_\infty$ algebra of the KP equation, free fermions and a 2-cocycle in the Lie algebra of pseudodifferential operators. Int. J. Mod. Phys. B, 11:3159-3193, 1997.
  56. A. Y. Orlov and P. Winternitz. Algebra of pseudodifferential oparators and symmetries of equations in the Kadomtsev-Petviashvili hierarchy . J. Math. Phys., 38:4644-4674, 1997.
  57. A. Sciarrino and P. Winternitz. Symmetries and solutions of the vector nonlinear Schrodinger equation. Nuovo Cim. , 112 B(6):853-871, 1997.
  58. D. Levi, L. Vinet, and P. Winternitz. Lie group formalism for difference equations. J. Phys. A, 30:633--649, 1997.
  59. M. Ait Abdelmalek, X. Leng, J. Patera, and P. Winternitz. Grading refinements in the contractions of Lie algebras and their invariants. J. Phys. A, 29:7519-7543, 1996.
  60. F. Gungor, M. Sanielevici, and P. Winternitz. On the integrability properties of variable coefficient Korteweg-de Vries equations . Can. J. Phys., 74:676-684, 1996.
  61. D. Levi and P. Winternitz. Symmetries of discrete dynamical systems. J. Math. Phys., 37:5551-5576, 1996.
  62. A. A. Izmest'ev, G. Pogosyan, A. Sissakian, and P. Winternitz. Contractions of Lie algebras and separations of variables . J. Phys. A, 29:5940-5962, 1996.
  63. S. Lafortune and P. Winternitz. Superposition formulas for pseudounitary Riccati equations. J. Math. Phys., 37:1539-1550, 1996.
  64. A. Grundland, P. Winternitz, and W. Zakrzewski. On the solution of the $ CP^1$ model in $(2+1)$ dimensions. J. Math. Phys., 37:1501-1520, 1996.
  65. M. del Olmo, M. Rodriguez, and P. Winternitz. The conformal group and integrable systems on a Lorentzian hyperboloid . Fortschr. der Physik, 44:90-125, 1996.
  66. J. Harnad and P. Winternitz. Classical and quantum integrable systems in $\widetildegl(2)^+$ and separation of variables . Commun. Math. Phys., 172:263-285, 1995.
  67. J. C. Ndgomo and P. Winternitz. Generalized Casimir operators of solvable Lie algebras with Abelian nilradicals. J. Phys. A, 27:2787-2800, 1994.
  68. E. G. Kalnins and P. Winternitz. Maximal Abelian subalgebras of complex Euclidean Lie algebras. Canad. J. Phys., 72:389-404, 1994.
  69. D. Levi, C. R. Menyuk, and P. Winternitz. Similarity reduction and perturbation solution of the stimulated Raman scattering equations in the presence of dissipation. Phys. Rev. A, 49:2844--2852, 1994.
  70. J. C. Ndogmo and P. Winternitz. Solvable lie algebras with abelian nilradicals. J. Phys. A, 27:405-423, 1994.
  71. D. Levi, L. Vinet, and P. Winternitz. Symmetries of a nonrelativistic Chern-Simons systems. Ann. of Phys., 229:101-117, 1994.
  72. P. LaFrance, F. Lehar, B. Loiseau, and P. Winternitz. Antinucleon -nucleon and nucleon-nucleon total cross sections and elastic scattering observables at all energies. Acta Polytechnica , 33(5):5-30, 1993.
  73. L. Gagnon and P. Winternitz. Symmetry classes of variable coefficient nonlinear Schrodinger equations. J. Phys. A , 26:7061-7076, 1993.
  74. G. Rideau and P. Winternitz. Representations of the quantum algebra $su(2)_q$ on a real two dimensional sphere. J. Math. Phys., 34:6030-6044, 1993.
  75. M. Faucher and P. Winternitz. Symmetry analysis of the Infeld-Rowlands equation. Phys. Rev. E, 48:3066-3071, 1993.
  76. M. A. del Olmo, M. A. Rodriguez, and P. Winternitz. Integrable systems based on $SU(p,q)$ homogeneous manifolds. J. Math. Phys., 34:5118-5139, 1993.
  77. D. Levi and P. Winternitz. Symmetries and conditional symmetries of differential-difference equations. J. Math. Phys. , 34:3713-3730, 1993.
  78. A. M. Grundland, J. Tuszynski, and P. Winternitz. Group theory and solutions of classical field theories with polynomial nonlinearities . Foundations of Physics, 23:633-665, 1993.
  79. K. Tenenblat and P. Winternitz. On the symmetry groups of the intrinsic generalized wave and sine-Gordon equations. J. Math. Phys., 34:3527-3542, 1993.
  80. J. Rubin and P. Winternitz. Solvable Lie algebras with Heisenberg ideals. J. Phys. A, 26:1123-1138, 1993.
  81. G. Rideau and P. Winternitz. Invariant nonlinear Schr\"odinger equations in two-dimensional space-time. J. Math. Phys. , 34:558-569, 1993.
  82. M. Kibler, G. H. Lamot, and P. Winternitz. Classical trajectories for two ring-shaped potentials. Int. J. Quantum Chem., 43:625-645, 1992.
  83. L. Martina, G. Soliani, and P. Winternitz. Partially invariant solutions of a class of nonlinear Schrodinger equations . J. Phys. A, 25:4425-4435, 1992.
  84. J. P. Gazeau and P. Winternitz. Symmetries of variable-coefficient Korteweg-de Vries equations. J. Math. Phys., 33:4087-4102, 1992.
  85. P. Lafrance, F. Lehar, B. Loiseau, and P. Winternitz. Antinucleon-nucleon scattering formalism and possible tests of CPT invariance . Helv. Phys. Acta, 65:611-640, 1992.
  86. L. Martina and P. Winternitz. Partially invariant solutions of nonlinear Klein-Gordon and Laplace equations,. J. Math. Phys., 33:2718-2727, 1992.
  87. V. Hussin, P. Winternitz, and H. Zassenhaus. Maximal Abelian subalgebras of pseudoorthogonal Lie algebras. Linear Algebra Appl., 173:125-163, 1992.
  88. S. Melkonian and P. Winternitz. Symmetry properties and solutions of nonlinear dispersive thin-film equations in three dimensions . J. Math. Phys., 32:3213-3222, 1991.
  89. P. Winternitz, A. M. Grundland, and J. A. Tuszynski. Nonlinear magnetization processes in the Landau-Ginzburg model of magnetic inhomogeneities for uniaxial ferromagnetics. Phys. Rev. B , 44:10040-10049, 1991.
  90. D. Levi, C. R. Menyuk, and P. Winternitz. Exact solutions of the stimulated Raman scattering equations. Phys. Rev. A , 44:6057-6070, 1991.
  91. E. Infeld, G. Rowlands, and P. Winternitz. Stability analysis for the quartic Landau-Ginzburg model \textupII. J. Phys. Cond. Matter, 3:4187-4193, 1991.
  92. B. Champagne, W. Hereman, and P. Winternitz. The computer calculation of Lie point symmetries of large systems of differential equations . Comput. Phys. Comm., 66:319-340, 1991.
  93. P. A. Clarkson and P. Winternitz. Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation. Phys. D , 49:257-272, 1991.
  94. M. Couture, J. Patera, R. T. Sharp, and P. Winternitz. Graded contractions of sl(3,D)$. J. Math. Phys., 32:2310-2318, 1991.
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