P. Winternitz

发表

On the Identification of a Lie Algebra Given by its Structure Constants

Douglas S. Rand, Hans Zassenhaus, D. W. Rand, 1988 .

Systems of ordinary differential equations with nonlinear superposition principles

R. Anderson, P. Winternitz, J. Harnad, 1982 .

Superposition laws for solutions of differential matrix Riccati equations arising in control theory

M. Sorine, P. Winternitz, 1985 .

Everything you always wanted to know about SU(3) ⊃ 0(3)

R. T. Sharp, M. Moshinsky, J. Patera, 1975 .

Subalgebras of real three‐ and four‐dimensional Lie algebras

Jiří Patera, Pavel Winternitz, J. Patera, 1977 .

Classification of systems of nonlinear ordinary differential equations with superposition principles

P. Winternitz, S. Shnider, 1984 .

Nonlinear superposition principles: a new numerical method for solving matrix Riccati equations

D. W. Rand, Pavel Winternitz, D. Rand, 1984 .

Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras

P. Winternitz, S. Shnider, 1984 .

On the integrability of systems of nonlinear ordinary differential equations with superposition principles

Tassos Bountis, Pavel Winternitz, T. Bountis, 1986 .

The Korteweg–de Vries equation and its symmetry-preserving discretization

P. Winternitz, Alexander Bihlo, Xavier Coiteux-Roy, 2014, 1409.4340.

Continuous symmetries of difference equations

D. Levi, P. Winternitz, 2005, nlin/0502004.

The computer calculation of Lie point symmetries of large systems of differential equations

Willy Hereman, Benoit Champagne, Pavel Winternitz, 1991 .

Symmetry Reduction and Exact Solutions of Nonlinear Partial Differential Equations

P. Clarkson, P. Winternitz, 1999 .

Discretization of partial differential equations preserving their physical symmetries

P. Winternitz, F. Valiquette, 2005, math-ph/0507061.

Lie groups, singularities and solutions of nonlinear partial differential equations

P. Winternitz, 2003 .

Lie symmetries of a generalised non-linear Schrodinger equation. III. Reductions to third-order ordinary differential equations

A. Ramani, B. Grammaticos, P. Winternitz, 1989 .

Lie group analysis of a generalized Krichever-Novikov differential-difference equation

D. Levi, P. Winternitz, Eugenio Ricca, 2014, 1401.6991.

The optical group and its subgroups

P. Winternitz, M. Perrin, J. Patera, 1978 .

Superintegrability in a two-dimensional space of nonconstant curvature

P. Winternitz, E. Kalnins, J. Kress, 2001, math-ph/0108015.

Quantum superintegrability and exact solvability in n dimensions

Miguel A. Rodriguez, P. Winternitz, Miguel A. Rodríguez, 2001, math-ph/0110018.

A class of solvable Lie algebras and their Casimir invariants

P. Winternitz, L. Šnobl, 2004, math-ph/0411023.

Comments on superposition rules for nonlinear coupled first‐order differential equations

P. Winternitz, 1984 .

Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups

R. T. Sharp, H. Zassenhaus, J. Patera, 1977 .

Group foliation and non-invariant solutions of the heavenly equation

P. Winternitz, L. Martina, M. Sheftel, 2001, math-ph/0108004.

1 2 A pr 2 00 2 Symmetry Classification of Diatomic Molecular Chains

S. Lafortune, P. Winternitz, S. Tremblay, 2022 .

Periodicity and quasi-periodicity for super-integrable Hamiltonian systems

P. Winternitz, M. Kibler, 1990, quant-ph/0405017.

Elementary Particle Reactions and the Lorentz and Galilei Groups

R. T. Sharp, J. Patera, P. Winternitz, 1975 .

Symmetries of Discrete Systems

P. Winternitz, 2003, nlin/0309058.

Exact solvability of superintegrable systems

P. Tempesta, P. Winternitz, A. Turbiner, 2000, hep-th/0011209.

Lorentz and Galilei Invariance on Lattices

P. Tempesta, D. Levi, P. Winternitz, 2003, hep-th/0310013.

Superintegrability with third-order integrals in quantum and classical mechanics

S. Gravel, P. Winternitz, 2002, math-ph/0206046.

Integrable Systems: From Classical to Quantum

G. Sabidussi, P. Winternitz, J. Harnad, 2000 .

Superintegrable systems in Darboux spaces

W. Miller, P. Winternitz, E. Kalnins, 2003, math-ph/0307039.

SEPARATION OF VARIABLES AND LIE-ALGEBRA CONTRACTIONS. APPLICATIONS TO SPECIAL FUNCTIONS

P. Winternitz, G. Pogosyan, A. Sissakian, 2003, math-ph/0310011.

The nucleon-nucleon triple scattering parameters for recoil particles

P. Winternitz, F. Lehár, Y. Kazarinov, 1968 .

ELASTIC SCATTERING OF NUCLEONS ON A TARGET WITH SPIN 1

P. Winternitz, 1961 .

Nonlinear equations with superposition formulas and exceptional group G2. III. The superposition formulas

V. Hussin, P. Winternitz, L. Gagnon, 1988 .

Subgroups of the Poincaré group and their invariants

R. T. Sharp, H. Zassenhaus, J. Patera, 1976 .

Canonical transformation and accidental degeneracy. III. A unified approach to the problem

M. Moshinsky, J. Patera, P. Winternitz, 1975 .

Polynomial irreducible tensors for point groups

R. T. Sharp, J. Patera, P. Winternitz, 1978 .

Weak transversality and partially invariant solutions

P. Tempesta, P. Winternitz, A. Grundland, 2002, math-ph/0206003.

Fourth order superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials

P. Winternitz, I. Marquette, Masoumeh Sajedi, 2017, 1703.09751.

The Conformal Group SU(2, 2) and Integrable Systems on a Lorentzian Hyperboloid

Mariano A. del Olmo, P. Winternitz, M. Rodŕıguez, 1994, hep-th/9407080.

Continuous symmetries of difference equations

D. Levi, P. Winternitz, 2005, nlin/0502004.

Classical and quantum integrable systems in 263-1263-1263-1and separation of variables

P. Winternitz, J. Harnad, 1993, hep-th/9312035.

Integrable Hamiltonian Systems With Velocity Dependent Potentials

B. Dorizzi, A. Ramani, B. Grammaticos, 1985 .

Solutions of (2+1)-dimensional spin systems

W. Zakrzewski, P. Winternitz, Z. Thomova, 1996, solv-int/9612003.

Polarization phenomena in nucleon-nucleon forward scattering

P. Winternitz, F. Perrot, F. Lehár, 1980 .

Hyperspherical Harmonics, Separation of Variables and the Bethe Ansatz

P. Winternitz, J. Harnad, 1994, hep-th/9405085.

Lie group classification of second-order ordinary difference equations

Roman Kozlov, Vladimir Dorodnitsyn, Pavel Winternitz, 2000 .

Symmetries of discrete dynamical systems involving two species

S. Lafortune, P. Winternitz, D. Gómez‐Ullate, 1998, solv-int/9812019.

Symmetries of discrete dynamical systems

D. Levi, P. Winternitz, 1996 .

Continuous symmetries of Lagrangians and exact solutions of discrete equations

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2003, nlin/0307042.

Symmetries, Lagrangian Formalism and Integration of Second Order Ordinary Difference Equations

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2003 .

Lie point symmetries and commuting flows for equations on lattices

D. Levi, P. Winternitz, 2001, math-ph/0112007.

Lie symmetries of multidimensional difference equations

D. Levi, P. Winternitz, S. Tremblay, 2001, 0709.3238.

Symmetry Classification of Diatomic Molecular Chains

S. Lafortune, P. Winternitz, S. Tremblay, 2001, nlin/0204021.

Relation between Bäcklund transformations and higher continuous symmetries of the Toda equation

Miguel A. Rodriguez, D. Levi, P. Winternitz, 2001 .

Lie point symmetries of difference equations and lattices

D. Levi, P. Winternitz, S. Tremblay, 2000, 0709.3112.

Point symmetries of generalized Toda field theories: II. Symmetry reduction

S. Lafortune, P. Winternitz, L. Martina, 2000, nlin/0004023.

Point Symmetries of Generalized Toda Field Theories

S. Lafortune, P. Winternitz, L. Martina, 2000, nlin/0004022.

Point Symmetries of Generalized Toda Field Theories II Applications of the Symmetries

S. Lafortune, P. Winternitz, L. Martina, 2000 .

Symmetries of the discrete Burgers equation

D. Levi, P. Winternitz, R. H. Heredero, 1999 .

Lie group formalism for difference equations

Luc Vinet, Decio Levi, Pavel Winternitz, 1997 .

Symmetries and Integrability of Difference Equations

Peter J. Olver, Decio Levi, Pavel Winternitz, 1999 .

Symmetries and conditional symmetries of differential difference equations

D. Levi, P. Winternitz, 1993 .

Symmetries of variable coefficient Korteweg–de Vries equations

Jean-Pierre Gazeau, Pavel Winternitz, J. Gazeau, 1992 .

Continuous symmetries of discrete equations

D. Levi, P. Winternitz, 1991 .

Lie point symmetries and ODEs passing the Painlevé test

D. Levi, P. Winternitz, D. Sekera, 2017, Journal of Nonlinear Mathematical Physics.

Fourth order superintegrable systems separating in polar coordinates. I. Exotic potentials

A. M. Escobar-Ruiz, P. Winternitz, J. C. Lopez Vieyra, 2017, 1706.08655.

Structures in proton-proton scattering at intermediate energies

A. Penzo, J. Yonnet, C. Newsom, 1984 .

Analysis of the energy dependence of proton-proton total cross-sections in terms ofO4 expansions

P. Winternitz, J. Bystrický, F. Perrot, 1986 .

Scattering formalism for nonidentical spinor particles

P. Winternitz, 1980 .

Formalism of Nucleon-Nucleon Elastic Scattering Experiments

P. Winternitz, J. Bystrický, F. Lehár, 1978 .

Energy dependence of nucleon-nucleon inelastic total cross-sections

T. Siemiarczuk, J. Bystricky, Pavel Winternitz, 1987 .

Exact results in the three-dimensional Landau-Ginzburg model of magnetic inhomogeneities in uniaxial ferromagnets: I. Continuous transitions

J. Tuszynski, P. Winternitz, A. Grundland, 1988 .

A superintegrable time-dependent system with kac-moody symmetry

P. Winternitz, Jamil Daboul, 2002 .

Time-dependent realization of the infinite-dimensional hydrogen algebra

P. Winternitz, Jamil Daboul, 2001 .

Tensor fields invariant under subgroups of the conformal group of space‐time

P. Winternitz, J. Harnad, J. Beckers, 1978 .

Invariants of real low dimension Lie algebras

R. T. Sharp, H. Zassenhaus, J. Patera, 1976 .

Classification and Identification of Lie Algebras

Pavel Winternitz, P. Winternitz, L. Šnobl, 2014 .

Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces

P. Winternitz, E. Kalnins, C. Boyer, 1983 .

Graded contractions of the Lie algebra e(2, 1)

J. Patera, P. Winternitz, G. Pogosyan, 1999 .

All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n − 1

P. Winternitz, L. Šnobl, 2008, 0809.3259.

Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)

Jiri Patera, B. R. Judd, Willard Miller, 1974 .

Grading refinements in the contractions of Lie algebras and their invariants

J. Patera, P. Winternitz, X. Leng, 1996 .

Invariants of the nilpotent and solvable triangular Lie algebras

P. Winternitz, S. Tremblay, 2001, 0709.3116.

Generalized Casimir operators of solvable Lie algebras with Abelian nilradicals

P. Winternitz, J. Ndogmo, 1994 .

Solvable Lie algebras with Heisenberg ideals

P. Winternitz, J. Rubin, 1993 .

Graded contractions of sl(3,C)

R. T. Sharp, J. Patera, P. Winternitz, 1991 .

Subgroups of the Euclidean group and symmetry breaking in nonrelativistic quantum mechanics

Pavel Winternitz, J. Patera, P. Winternitz, 1977 .

Higher Order Quantum Superintegrability: A New “Painlevé Conjecture”

P. Winternitz, I. Marquette, 2019, Integrability, Supersymmetry and Coherent States.

Superintegrable systems with spin induced by co-algebra symmetry

P. Winternitz, O. Gingras, D. Riglioni, 2013, 1312.3273.

Nonlinear differential equations and lie superalgebras

V. Hussin, P. Winternitz, L. Gagnon, 1987 .

Contractions of Lie algebras and separation of variables

P. Winternitz, A. A. Izmest'ev, G. Pogosyan, 1996 .

Classical and quantum superintegrability with applications

W. Miller, P. Winternitz, S. Post, 2013, 1309.2694.

A systematic search for nonrelativistic systems with dynamical symmetries

P. Winternitz, A. Makarov, J. A. Smorodinsky, 1967 .

ON HIGHER SYMMETRIES IN QUANTUM MECHANICS

P. Winternitz, Ya. A. Smorodinsky, M. Uhlíř, 1965 .

The Group $O(4)$, Separation of Variables and the Hydrogen Atom

W. Miller, P. Winternitz, E. Kalnins, 1976 .

Second-order delay ordinary differential equations, their symmetries and application to a traffic problem

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2019 .

Lie group classification of second-order delay ordinary differential equations

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2019, 1901.06251.

Lie group classification of first-order delay ordinary differential equations

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2017, 1712.02581.

Solvable Lie algebras with triangular nilradicals

P. Winternitz, S. Tremblay, 1998, 0709.3581.

Solvable Lie algebras with Abelian nilradicals

P. Winternitz, J. Ndogmo, 1994 .

Evolution equations invariant under two-dimensional space-time Schrödinger group

P. Winternitz, G. Rideau, 1993 .

Continuous subgroups of the fundamental groups of physics. I. General method and the Poincaré group

Jiří Patera, H. Zassenhaus, Pavel Winternitz, 1975 .

Contact transformations for difference schemes

D. Levi, P. Winternitz, C. Scimiterna, 2011, 1110.3409.

Can phase shift analysis above the inelastic threshold provide unambiguous results

P. Winternitz, J. Bystrický, F. Lehár, 1979 .

Group invariant solutions for the N=2 super Korteweg–de Vries equation

M. Ayari, V. Hussin, P. Winternitz, 1999 .

Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation

Peter A. Clarkson, Pavel Winternitz, P. Clarkson, 1991 .

Non-classical symmetry reduction: example of the Boussinesq equation

Decio Levi, Pavel Winternitz, D. Levi, 1989 .

On the infinite‐dimensional symmetry group of the Davey–Stewartson equations

Benoit Champagne, Pavel Winternitz, B. Champagne, 1988 .

Lie symmetries of a generalised non-linear Schrodinger equation. II. Exact solutions

P. Winternitz, L. Gagnon, 1989 .

Lie symmetries of a generalised nonlinear Schrodinger equation: I. The symmetry group and its subgroups

Pavel Winternitz, P. Winternitz, L. Gagnon, 1988 .

Definitions and Predictions of Integrability for Difference Equations

P. Olver, J. Hietarinta, D. Levi, 2011 .

Symmetry Groups of Multidimensional Integrable Nonlinear Systems

P. Winternitz, 1990 .

Equations invariant under the symmetry group of the Kadomtsev-Petviashvili equation

D. Levi, P. Winternitz, Pavel Winternitz, 1988 .

Lie algebra contractions and symmetries of the Toda hierarchy

D. Levi, P. Winternitz, R. H. Heredero, 2000 .

P∞ algebra of symmetries of the kadomtsev-petviashvili equation, free fermions, and 2-cocycles in the lie algebra of pseudo-differential operatorsalgebra of symmetries of the kadomtsev-petviashvili equation, free fermions, and 2-cocycles in the lie algebra of pseudo-differential operators

A. Orlov, P. Winternitz, 1997 .

P ALGEBRA OF KP, FREE FERMIONS AND 2-COCYCLE IN THE LIE ALGEBRA OF PSEUDODIFFERENTIAL OPERATORS

A. Orlov, P. Winternitz, 1997, solv-int/9701008.

Are all the equations of the Kadomtsev–Petviashvili hierarchy integrable?

Alfred Ramani, B. Grammaticos, B. Dorizzi, 1986 .

Spherical type integrable classical systems in a magnetic field

A. Marchesiello, P. Winternitz, L. Šnobl, 2018 .

Three-dimensional superintegrable systems in a static electromagnetic field

A. Marchesiello, P. Winternitz, L. Šnobl, 2015, 1507.04632.

Cylindrical type integrable classical systems in a magnetic field

P. Winternitz, L. Šnobl, F. Fournier, 2019, Journal of Physics A: Mathematical and Theoretical.

Two-dimensional superintegrable systems from operator algebras in one dimension

P. Winternitz, I. Marquette, M. Sajedi, 2018, Journal of Physics A: Mathematical and Theoretical.

Superintegrable systems with spin and second-order integrals of motion

P. Winternitz, J. Désilets, I. Yurdusen, 2012, 1208.2886.

Integrable and superintegrable systems with spin in three-dimensional Euclidean space

P. Winternitz, I. Yurdusen, 2009, 0906.1021.

An infinite family of solvable and integrable quantum systems on a plane

P. Winternitz, A. Turbiner, F. Tremblay, 2009, 0904.0738.

Reduction of superintegrable systems: the anisotropic harmonic oscillator.

P. Tempesta, P. Winternitz, Miguel A. Rodríguez, 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

Quasiseparation of variables in the Schrödinger equation with a magnetic field

P. Winternitz, F. Charest, C. Hudon, 2005, math-ph/0502046.

Integrable and superintegrable quantum systems in a magnetic field

P. Winternitz, J. Bérubé, 2003, math-ph/0311051.

Integrable and superintegrable Hamiltonian systems in magnetic fields

P. Winternitz, Eric McSween, 2000 .

A new basis for the representations of the rotation group. Lamé and Heun polynomials

P. Winternitz, J. Patera, 1973 .

Group theoretical analysis of dispersive long wave equations in two space dimensions

Pavel Winternitz, P. Winternitz, G. Paquin, 1990 .

LIE GROUPS AND SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS

P. Winternitz, 1983 .

Algebra of pseudodifferential operators and symmetries of equations in the Kadomtsev–Petviashvili hierarchy

A. Orlov, P. Winternitz, 1997 .

Group Theory and exact Solutions of Partially Integrable Differential Systems

P. Winternitz, 1990 .

The cylindrical Kadomtsev-Petviashvili equation; its Kac-Moody-Virasoro algebra and relation to KP equation

Decio Levi, Pavel Winternitz, D. Levi, 1988 .

Symmetry reduction for the Kadomtsev–Petviashvili equation using a loop algebra

Decio Levi, D. Levi, P. Winternitz, 1986 .

Symmetries of the self‐dual Einstein equations. I. The infinite‐dimensional symmetry group and its low‐dimensional subgroups

Charles P. Boyer, P. Winternitz, P. Winternitz, 1989 .

Heisenberg algebra, umbral calculus and orthogonal polynomials

G. Dattoli, G. Dattoli, D. Levi, 2007, 0712.2957.

POLARIZED PROTON TARGETS AND LOW-ENERGY NUCLEON--NUCLEON EXPERIMENTS.

P. Winternitz, F. Lehar, 1967 .

Angular distribution of gamma quanta in the capture of polarized μ−-mesons by atomic nuclei

P. Winternitz, F. Janouch, 1962 .

On bases for irreducible representations of O (3) suitable for systems with an arbitrary finite symmetry group

P. Winternitz, J. Patera, 1976 .

Critical review of the present experimental status of neutron-proton scattering up to 1 GeV

P. Winternitz, J. Bystrický, C. Lechanoine-Leluc, 1987 .

Symmetry breaking interactions for the time dependent Schrödinger equation

R. T. Sharp, P. Winternitz, P. Winternitz, 1976 .

Nonlinear action of Lie groups and superposition principles for nonlinear differential equations

P. Winternitz, 1982 .

Simultaneous phase shift analysis of 210 MeV nucleon-nucleon scattering

P. Winternitz, F. Lehár, Y. Kazarinov, 1968 .

Direct reconstruction of pp elastic scattering amplitudes from experimental data between 0.83 and 2.7 GeV

C. Lac, P. Winternitz, J. Bystrický, 1990 .

Painlevé transcendents : their asymptotics and physical applications

D. Levi, P. Winternitz, 1992 .

Symmetry classes of variable coefficient nonlinear Schrodinger equations

Pavel Winternitz, P. Winternitz, L. Gagnon, 1993 .

New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates

A. M. Escobar-Ruiz, P. Winternitz, R. Linares, 2020, Journal of Physics A: Mathematical and Theoretical.

Lie Groups and Solutions of Nonlinear Partial Differential Equations

P. Winternitz, 1993 .

Partially invariant solutions of a class of nonlinear Schrodinger equations

P. Winternitz, G. Soliani, L. Martina, 1992 .

Partially invariant solutions of nonlinear Klein–Gordon and Laplace equations

P. Winternitz, L. Martina, 1992 .

Conditional symmetries and conditional integrability for nonlinear systems

P. Winternitz, 1991 .

Physical Applications of Painlevé Type Equations Quadratic in the Highest Derivatives

P. Winternitz, 1992 .

Fifth-order superintergrable quantum system separating in Cartesian coordinates. Doubly exotic potentials

P. Winternitz, Ismail Abouamal, 2017, 1708.03379.

Exact solutions of the multidimensional classical φ6‐field equations obtained by symmetry reduction

J. Tuszynski, P. Winternitz, A. Grundland, 1987 .

Bäcklund transformations and the infinite-dimensional symmetry group of the Kadomtsev-Petviashvili equation

D. Levi, P. Winternitz, D. David, 1986 .

Generalized Kadomtsev–Petviashvili equation with an infinite-dimensional symmetry algebra

P. Winternitz, F. Gungor, 2001, nlin/0109009.

Exact solutions of the spherical quintic nonlinear Schrödinger equation

P. Winternitz, L. Gagnon, 1989 .

New classes of exact solutions of the 6 model in 3+1 dimensions

J. Tuszynski, P. Winternitz, A. Grundland, 1987 .

Superintegrable systems with spin and second-order tensor and pseudo-tensor integrals of motion

İsmet Yurduşen, O Oğulcan Tuncer, Pavel Winternitz, 2021, Journal of Physics A: Mathematical and Theoretical.

General Nth-order superintegrable systems separating in polar coordinates

A. M. Escobar-Ruiz, P. Winternitz, I. Yurdusen, 2018, Journal of Physics A: Mathematical and Theoretical.

Fourth-order superintegrable systems separating in polar coordinates. II. Standard potentials

A. M. Escobar-Ruiz, P. Winternitz, J. C. L. Vieyra, 2018, Journal of Physics A: Mathematical and Theoretical.

Third-order superintegrable systems separating in polar coordinates

P. Winternitz, F. Tremblay, 2010, 1002.1989.

Superintegrability with second- and third-order integrals of motion

P. Winternitz, 2009 .

Superintegrable systems with third-order integrals of motion

P. Winternitz, I. Marquette, 2007, 0711.4783.

Continuous Symmetries of Differential-Difference Equations

D. Levi, P. Winternitz, 1995 .

Bäcklund and Darboux transformations : the geometry of solitons : AARMS-CRM Workshop, June 4-9, 1999, Halifax, N.S., Canada

C. Rogers, R. Milson, A. Coley, 2001 .

ODEPAINLEVE - A MACSYMA package for painlevé analysis of ordinary differential equations

D. W. Rand, Pavel Winternitz, D. Rand, 1986 .

Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles

Mariano A. del Olmo, P. Winternitz, M. Rodríguez, 1986 .

Superposition principles for matrix Riccati equations

R. L. Anderson, P. Winternitz, J. Harnad, 1983 .

Group Theory and Numerical Analysis

P. Olver, G. Quispel, A. Iserles, 2005 .

Lie-Theoretical Generalization and Discretization of the Pinney Equation☆

Wolfgang K. Schief, Pavel Winternitz, Colin Rogers, 1997 .

On the relation between weak and strong invariance of differential equations

M. Olmo, P. Winternitz, J. Cariñena, 1993 .

General Nth order integrals of motion in the Euclidean plane

P. Winternitz, S. Post, 2015 .

Polynomial Poisson algebras for classical superintegrable systems with a third-order integral of motion

P. Winternitz, I. Marquette, 2006, math-ph/0608021.

SOLITONS IN SHALLOW SEAS OF VARIABLE DEPTH AND IN MARINE STRAITS

Decio Levi, Pavel Winternitz, D. Levi, 1989 .

Equivalence Classes and Symmetries of the Variable Coefficient Kadomtsev—Petviashvili Equation

F. Güngör, P. Winternitz, F. Güngör, 2004 .

On the integrability properties of variable coefficient Korteweg-de Vries equations

P. Winternitz, F. Güngör, M. Sanielevici, 1996 .

Integrable Nonlinear Equations for Water Waves in Straits of Varying Depth and Width

Decio Levi, Pavel Winternitz, D. Levi, 1987 .

Third-order superintegrable systems separable in parabolic coordinates

P. Winternitz, S. Post, I. Popper, 2012, 1204.0700.

An infinite family of superintegrable deformations of the Coulomb potential

P. Winternitz, S. Post, 2010, 1003.5230.

Periodic orbits for an infinite family of classical superintegrable systems

P. Winternitz, A. Turbiner, F. Tremblay, 2009, 0910.0299.

Classical and Quantum Superintegrable Systems with N-th Order Integrals of Motion

P. Winternitz, S. Post, 2015 .

General Nth order integrals of the motion

P. Winternitz, S. Post, 2015, 1501.00471.

Infinite families of superintegrable systems separable in subgroup coordinates

P. Winternitz, S. Post, D. Lévesque, 2012, 1207.6976.

A nonseparable quantum superintegrable system in 2D real Euclidean space

P. Winternitz, S. Post, 2011, 1101.5405.

Superintegrable systems in quantum mechanics and classical Lie theory

P. Tempesta, P. Winternitz, M. Sheftel, 2001 .

Symmetry reduction and superintegrable Hamiltonian systems

P. Tempesta, P. Winternitz, M. Rodríguez, 2009, 0906.3396.

Superintegrability in Classical and Quantum Systems

W. Miller, P. Tempesta, P. Winternitz, 2004 .

Integrable and superintegrable systems with spin

P. Winternitz, I. Yurdusen, 2006, math-ph/0604050.

Discrete matrix Riccati equations with superposition formulas

P. Winternitz, A. Penskoi, 2003, math-ph/0305053.

Group theory and solutions of classical field theories with polynomial nonlinearities

P. Winternitz, A. Grundland, J. Tuszynski, 1993 .

Dynamical invariance algebra of the Hartmann potential

P. Winternitz, M. Kibler, 1987 .

Erratum: “A class of superintegrable systems of Calogero type” [J. Math. Phys. 47, 093505 (2006)]

P. Winternitz, R. Smirnov, 2007 .

A class of superintegrable systems of Calogero type

P. Winternitz, R. Smirnov, 2006, math-ph/0606006.

Classical trajectories for two ring‐shaped potentials

P. Winternitz, M. Kibler, G. Lamot, 1992, quant-ph/9810006.

Periodicity and quasi-periodicity for super-integrable Hamiltonian systems

P. Winternitz, M. Kibler, 1990, quant-ph/0405017.

Lie algebras under constraints and non-bijective canonical transformations

P. Winternitz, M. Kibler, 1988 .

Subgroups of Lie groups and separation of variables

W. Miller, J. Patera, P. Winternitz, 1981 .

Pseudopotentials and Lie symmetries for the generalized nonlinear Schrödinger equation

P. Winternitz, J. Harnad, 1982 .

un 2 00 2 Weak Transversality and Partially Invariant Solutions

P. Tempesta, P. Winternitz, A. Grundland, 2002 .

Erratum: Polynomial Poisson Algebras for Classical Superintegrable Systems with a Third Order Integral of Motion [J. Math. Phys. 48, 012902 (2007)]

P. Winternitz, I. Marquette, 2008 .

Difference schemes with point symmetries and their numerical tests

P. Winternitz, A.Bourlioux, C. Cyr-Gagnon, 2006, math-ph/0602057.

Solutions of Nonlinear Differential and Difference Equations with Superposition Formulas

Alexander V. Turbiner, Pavel Winternitz, P. Winternitz, 1999, solv-int/9905003.

Discretizing families of linearizable equations

A. Ramani, B. Grammaticos, P. Winternitz, 1998 .

Superposition formulas for rectangular matrix Riccati equations

Mariano A. del Olmo, P. Winternitz, M. Rodríguez, 1987 .

Conformally Invariant Elliptic Liouville Equation and Its Symmetry-Preserving Discretization

D. Levi, P. Winternitz, L. Martina, 2017, Theoretical and Mathematical Physics.

The classification of complete sets of operators commuting with the Dirac operator in Minkowski space-time

P. Winternitz, N. Kamran, R. McLenaghan, 1988 .

Symmetry reduction for nonlinear relativistically invariant equations

P. Winternitz, J. Harnad, A. Grundland, 1984 .

Yakov Abramovich Smorodinsky and his influence on my life

P. Winternitz, 2009 .

Symmetries of the Continuous and Discrete Krichever-Novikov Equation ⋆

D. Levi, P. Winternitz, R. Yamilov, 2011, 1110.5021.

Allowed transformations and symmetry classes of variable coefficient Korteweg-de Vries equations

J. Gazeau, P. Winternitz, 1992 .

Lie Point Symmetry Preserving Discretizations for Variable Coefficient Korteweg–de Vries Equations

Vladimir Dorodnitsyn, Pavel Winternitz, P. Winternitz, 2000 .

Symmetries and solutions of the vector nonlinear Schrödinger equation (

A. Sciarrino, P. Winternitz, 1997 .

Continuous subgroups of the fundamental groups of physics. II. The similitude group

Jiří Patera, H. Zassenhaus, Pavel Winternitz, 1975 .

Symmetries and nonlinear phenomena in physics

P. Winternitz, 2008 .

Lie symmetries and superintegrability in quantum mechanics

P. Tempesta, P. Winternitz, M. Sheftel, 2002 .

Umbral Calculus, Difference Equations and the

P. Tempesta, D. Levi, P. Winternitz, 2008 .

Umbral calculus, difference equations and the discrete Schrödinger equation

P. Tempesta, D. Levi, P. Winternitz, 2003, nlin/0305047.

Superintegrable Systems in Classical and Quantum Mechanics

P. Winternitz, 2004 .

Integrable systems based on SU(p,q) homogeneous manifolds

Mariano A. del Olmo, P. Winternitz, Miguel A. Rodríguez, 1993 .

MAXIMAL ABELIAN SUBALGEBRAS OF PSEUDOUNITARY LIE ALGEBRAS

Mariano A. del Olmo, H. Zassenhaus, P. Winternitz, 1990 .

Maximal abelian subalgebras of real and complex symplectic Lie algebras

H. Zassenhaus, J. Patera, P. Winternitz, 1983 .

Separation of variables for the Hamilton-Jacobi equation on complex projective spaces

P. Winternitz, E. Kalnins, C. Boyer, 1985 .

Subgroup Type Coordinates and the Separation of Variables in Hamilton-Jacobi and Schrödinger Equations

P. Winternitz, E. Kalnins, Z. Thomova, 2004, math-ph/0405063.

Separation of variables and subgroup bases on n-dimensional hyperboloids

P. Winternitz, G. Pogosyan, 2002 .

Contractions of Lie Algebras and Separation of Variables.. Two-Dimensional Hyperboloid

P. Winternitz, A. A. Izmest'ev, G. Pogosyan, 1997 .

Dimensional Reduction for Equations Involving Discrete and Continuous Variables

D. Levi, P. Winternitz, 1993 .

Symmetries of Differential Equations on a Lattice. An Example: The Toda Lattice

D. Levi, P. Winternitz, 1993 .

Symmetry properties and solutions of nonlinear dispersive thin‐film equations in three dimensions

P. Winternitz, S. Melkonian, 1991 .

P. Winternitz, 1991 .

Point symmetries of conditionally integrable nonlinear evolution equations

P. Winternitz, J. Rubin, 1990 .

Harmonics on hyperspheres, separation of variables and the bethe ansatz

P. Winternitz, J. Harnad, 1995 .

PASCAL programs for identification of lie algebras Part 2: SPLIT — a program to decompose parameter-free and parameter-dependent Lie algebras into direct sums

H. Zassenhaus, D. Rand, P. Winternitz, 1987 .

IN MEMORY OF YAKOV ABRAMOVICH SMORODINSKY

P. Winternitz, Ya. A. Smorodinsky, 2009 .

v 2 5 N ov 2 00 7 Integrable and superintegrable systems with spin

P. Winternitz, I. Yurdusen, 2008 .

MAXIMAL ABELIAN SUBALGEBRAS OF E(P, Q) ALGEBRAS

P. Winternitz, Z. Thomova, 1998, math/9805024.

Maximal Abelian subgroups of the isometry and conformal groups of Euclidean and Minkowski spaces

P. Winternitz, Z. Thomova, 1997, physics/9707005.

Maximal Abelian subalgebras of complex Euclidean Lie algebras

P. Winternitz, E. Kalnins, 1994 .

Maximal abelian subalgebras of pseudoorthogonal lie algebras

H. Zassenhaus, V. Hussin, P. Winternitz, 1992 .

Maximal abelian subalgebras of complex orthogonal lie algebras

H. Zassenhaus, V. Hussin, P. Winternitz, 1990 .

Quantum numbers for particles in de Sitter space

H. Zassenhaus, J. Patera, P. Winternitz, 1976 .

The maximal solvable subgroups of SO(p,q) groups

H. Zassenhaus, J. Patera, P. Winternitz, 1974 .

The maximal solvable subgroups of the SU(p,q) groups and all subgroups of SU(2,1)

H. Zassenhaus, J. Patera, P. Winternitz, 1974 .

Invariant trilinear couplings involving both SU(2) and SU(1, 1) states

P. Winternitz, J. Patera, 1973 .

Solvable Lie algebras with Borel nilradicals

P. Winternitz, L. Šnobl, 2011, 1110.5492.

Expansions of relativistic scattering amplitudes and harmonic analysis on the lorentz group

P. Winternitz, 1971 .

RELATIVISTIC TWO-VARIABLE EXPANSIONS FOR THREE-BODY DECAY AMPLITUDES.

H. R. Hicks, P. Winternitz, 1971 .

Two-dimensional expansions of relativistic amplitudes in the Mandelstam triangle and crossing symmetric reactions

P. Winternitz, 1969 .

Discrete two-variable expansions of scattering amplitudes for particles with spin

P. Winternitz, M. Daumens, 1980 .

Possible ambiguities in $pi$N phase-shift analysis

P. Winternitz, R. Brunet, L. Gauthier, 1976 .

Discrete Two Variable Expansions of Physical Scattering Amplitudes

J. Patera, P. Winternitz, J. Bystrický, 1976 .

Two-Variable Galilei-Group Expansions of Nonrelativistic Scattering Amplitudes

R. T. Sharp, J. Patera, P. Winternitz, 1973 .

Clebsch-Gordan Coefficients for the Coupling of SL(2, C) Principal-Series Representations

R. Ra̧czka, P. Winternitz, M. A. Rashid, 1970 .

Poincaré and Lorentz invariant expansions of relative amplitudes

P. Winternitz, J. Smorodinsky, M. Sheftel, 1968 .

SUBGROUPS OF LIE GROUPS AND SYMMETRY BREAKING

P. Winternitz, 1977 .

Recursion and Symmetry Relations for the Clebsch‐Gordan Coefficients of the Homogeneous Lorentz Group

R. Ra̧czka, P. Winternitz, M. A. Rashid, 1970 .

CLEBSCH--GORDAN COEFFICIENTS FOR THE LORENTZ GROUP. I. PRINCIPAL SERIES.

R. Ra̧czka, P. Winternitz, R. L. Anderson, 1967 .

KINEMATICS OF K/sub l3/ DECAY AMPLITUDES AND RELATIVISTIC EQUATIONS FOR SPIN-ZERO PARTICLES.

P. Winternitz, R. Willey, T. Yao, 1973 .

Group theoretical analysis of a rotating shallow liquid in a rigid container

C. Rogers, M. Nucci, D. Levi, 1989 .

Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2017, 1712.07837.

The adjoint equation method for constructing first integrals of difference equations

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2015 .

Crossing Symmetric Expansions of Physical Scattering Amplitudes; The O(2, 1) Group and Lamé Functions

P. Winternitz, N. Macfadyen, 1971 .

Bases for representations of quantum algebras

N. Atakishiyev, P. Winternitz, 2000 .

Superposition formulas for pseudounitary matrix Riccati equations

S. Lafortune, P. Winternitz, 1996 .

Normal forms of elements of classical real and complex Lie and Jordan algebras

Jiří Patera, H. Zassenhaus, Pavel Winternitz, 1983 .

Contractions of Lie algebras and separation of variables. The n -dimensional sphere

P. Winternitz, A. A. Izmest'ev, G. Pogosyan, 1999 .

Subgroup type coordinates in four-dimensional flat spaces

P. Winternitz, E. Kalnins, Z. Thomova, 2004 .

Erratum: Higher indices of group representations

R. T. Sharp, J. Patera, P. Winternitz, 1977 .

One‐Parameter Subgroups of Unitary Groups with Indefinite Metric and in Particular of the Conformal Group

P. Winternitz, J. Belinfante, 1971 .

Conformally Invariant Elliptic Liouville Equation and Its Symmetry-Preserving Discretization

D. Levi, P. Winternitz, L. Martina, 2018, Theoretical and Mathematical Physics.

Symmetry preserving discretization of ordinary differential equations. Large symmetry groups and higher order equations

Rutwig Campoamor-Stursberg, Pavel Winternitz, P. Winternitz, 2015, 1507.06428.

Structure preserving discretizations of the Liouville equation and their numerical tests

D. Levi, P. Winternitz, L. Martina, 2015, 1504.01953.

Lie-point symmetries of the discrete Liouville equation

D. Levi, P. Winternitz, L. Martina, 2014, 1407.4043.

Invariant difference schemes and their application to invariant ordinary differential equations

P. Winternitz, R. Rebelo, 2009, 0906.2980.

Lie symmetries and exact solutions of first-order difference schemes

P. Winternitz, Miguel A. Rodríguez, 2004, nlin/0402047.

Symmetry Preserving Discretization of SL(2,ℝ) Invariant Equations

A. Bourlioux, P. Winternitz, R. Rebelo, 2007, 0711.0145.

Discretization of partial differential equations preserving their physical symmetries

P. Winternitz, F. Valiquette, 2005, math-ph/0507061.

Ordinary di ff erential and di ff erence equations invariant under SL ( 2 , R ) and their solutions

P. Winternitz, R. Rebelo, 2009 .

Higher indices of group representations

R. T. Sharp, J. Patera, P. Winternitz, 1976 .

Optimal Complete and Optimal Sufficient Sets of Experiments for Elastic Nucleon-Nucleon Scattering

J. Patera, P. Winternitz, J. Bystrický, 1978 .

Quadratic Hamiltonians in phase space and their eigenstates

M. Moshinsky, P. Winternitz, 1980 .

Nonlinear equations with superposition formulas and the exceptional group G2. II. Classification of the equations

V. Hussin, P. Winternitz, J. Beckers, 1987 .

Maximal Abelian Subgroups of SU(p,q) and Integrable Hamiltonian Systems

Mariano A. del Olmo, P. Winternitz, Miguel A. Rodríguez, 1994 .

Invariant solutions of delay differential equations

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2018 .

Nonlinear equations invariant under the Poincaré, similitude, and conformal groups in two-dimensional space-time

P. Winternitz, G. Rideau, 1990 .

Subgroups of the similitude group of three-dimensional Minkowski space

R. T. Sharp, H. Zassenhaus, J. Patera, 1976 .

Solutions of the multidimensional Sine Gordon equation obtained by symmetry reduction

P. Winternitz, A. Grundland, J. Harnard, 1982 .

Symmetry Reduction for Nonlinear wave Equations in Riemannian and Pseudo-Riemannian Spaces

P. Winternitz, J. Harnad, A. Grundland, 1984 .

Nonlinear superposition formulas based on imprimitive group action

P. Winternitz, M. Havlíček, S. Posta, 1999 .

Group theoretical approach to superposition rules for systems of Riccati equations

P. Winternitz, J. Harnad, R. Anderson, 1981 .

Superposition formulas for nonlinear superequations

V. Hussin, P. Winternitz, L. Gagnon, 1990 .

Nonlinear equations with superposition formulas and the exceptional group G2. I. Complex and real forms of g2 and their maximal subalgebras

V. Hussin, P. Winternitz, J. Beckers, 1986 .

Complex parabolic subgroups of G2 and nonlinear differential equations

V. Hussin, P. Winternitz, J. Beckers, 1986 .

Integrability, chaos and nonlinear superposition formulas for differential matrix Riccati equations

Mariano A. del Olmo, P. Winternitz, M. Rodríguez, 1986 .

Discrete systems related to some equations of the Painlevé–Gambier classification

A. Ramani, B. Grammaticos, P. Winternitz, 2000, nlin/0104019.

Stability analysis for the quartic Landau-Ginzburg model. II

G. Rowlands, P. Winternitz, E. Infeld, 1990 .

A note on generalization of the Lewis invariant and the Ermakov systems

A. Strauss, P. Winternitz, F. Haas, 2017 .

Subgroups of Lie groups and symmetry reduction for nonlinear partial differential equations

P. Winternitz, J. Harnad, A. Grundland, 1984 .

Structure preserving discretizations of the Liouville equation and their numerical tests

D. Levi, P. Winternitz, L. Martina, 2015, 1504.01953.

Symmetries and Integrability of Difference Equations: Nonlinear difference equations with superposition formulae

P. Winternitz, 1999 .

Analysis and applications of the symmetry group of the multidimensional three-wave resonant interaction problem

Luigi Martina, P. Winternitz, P. Winternitz, 1989 .

Symmetries, Singularities and Exact Solutions for Nonlinear Systems

P. Winternitz, Pavel Winternitz, 1990 .

First integrals of difference equations which do not possess a variational formulation

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2014 .

First integrals of difference equations which do not possess a variational formulation

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2014, Doklady Mathematics.

First integrals of ordinary difference equations beyond Lagrangian methods

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2013, 1311.1597.

First integrals of ordinary difference equations which do not possess a variational formulation

P. Winternitz, V. Dorodnitsyn, R. Kozlov, 2013, 1307.7585.

Cohomology and symmetry of differential equations

M. Olmo, P. Winternitz, J. Cariñena, 1991 .

The computer calculation of Lie point symmetries of large systems of differential equations

W. Hereman, B. Champagne, P. Winternitz, 1991 .

Antiproton Annihilation into Two Mesons and Higher Symmetries

N. Hieu, P. Winternitz, A. Makarov, 1966, 1966.

CLASSICAL AND QUANTUM INTEGRABLE SYSTEMS IN GL(2)+* AND SEPARATION OF VARIABLES

P. Winternitz, J. Harnard, 1995 .

Invariant Solutions of Equations of the Hydrodynamic Type

P. Winternitz, A. Grundland, M. Sheftel, 2000 .

QUANTUM NUMBERS IN THE LITTLE GROUPS OF THE POINCARE GROUP.

P. Winternitz, Y. Smorodinskii, I. Lukach, 1966 .