Winternitz, Pavel
- Professeur émérite
-
Faculté des arts et des sciences - Département de mathématiques et de statistique
André-Aisenstadt
Courriels
Affiliations
- Membre Centre de recherches mathématiques
- Membre CRM Centre de recherches mathématiques
Expertise
- Super intégrabilité en mécanique classique et quantique
- Phénomènes discrets en physique
- Symétries des équations différentielles et aux différences
- Solitons
Physique mathématique, symétries et phénomènes non linéaires.
1.Applications de la théorie de groupes de Lie à l'étude des équations à différences finies
2.Solutions exactes des équations différentielles non-linéaires,
3.Contraction des algèbres de Lie et la séparation de variables
4.Classification des algèbres de Lie et leurs sous-algèbres
5.Systèmes intégrables et superintégrables en physique quantique et classique.
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Projets de recherche Tout déplier Tout replier
Group theory and nonlinear phenomena in physics CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2016 - 2022
CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2015 - 2023
GROUP THEORY AND NONLINEAR PHENOMENA IN PHYSICS / 2010 - 2015
CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2008 - 2016
GROUP THEORY AND NONLINEAR PHENOMENA IN PHYSICS CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 1994 - 2017
Publications choisies Tout déplier Tout replier
First integrals of difference equations that do not have a variational formulation
Superintegrable systems with spin induced by co-algebra symmetry
Classical and quantum superintegrability with applications
Continuous symmetries of Lagrangians and exact solutions of discrete equations
Infinite families of superintegrable systems separable in subgroup coordinates
Superintegrable systems with spin et second-order integrals of motion
Third-order superintegrable systems separable in parabolic coordinates
Solvable Lie algebras with Borel nilradicals
Contact transformations for difference schemes
Symmetries of the continuous and discrete Krichever-Novikov equation
Are there contact transformations for discrete equations?
A nonseparable quantum superintegrable system in 2D real Euclidean space
Lie point symmetries of differential-difference equations
Third-order superintegrable systems separating in polar coordinates
An infinite family of superintegrable deformations of the Coulomb potential
Periodic orbits for an infinite family of classical superintegrable systems
Invariant difference schemes and their application to ${\rm sl}(2,\Bbb R)$ invariant ordinary differential equations
Integrable and superintegrable systems with spin in three-dimensional Euclidean space
An infinite family of solvable and integrable quantum systems on a plane
All solvable extensions of a class of nilpotent Lie algebras of dimension $n$ and degree of nilpotency $n-1$
Reduction of superintegrable systems: the anisotropic harmonic oscillator
Symmetry preserving discretization of ${\rm SL}(2,\Bbb R)$ invariant equations
Superintegrable systems with third-order integrals of motion
Heisenberg algebra, umbral calculus and orthogonal polynomials
Erratum: ``Polynomial Poisson algebras for classical superintegrable systems with a third order integral of motion'' [J. Math. Phys. {\bf 48} (2007), no. 1, 012902, 16 pp.; MR2292612]
Erratum: ``A class of superintegrable systems of Calogero type'' [J. Math. Phys. {\bf 47} (2006), no. 9, 093505, 8 pp.; èfcno 2263659]
Polynomial Poisson algebras for classical superintegrable systems with a third-order integral of motion
Quasiseparation of variables in the Schrödinger equation with a magnetic field
Integrable and superintegrable systems with spin
A class of superintegrable systems of Calogero type
Difference schemes with point symmetries and their numerical tests
Continuous symmetries of difference equations
Discretization of partial differential equations preserving their physical symmetries
Subgroup type coordinates and the separation of variables in Hamilton-Jacobi and Schrödinger equations
A class of solvable Lie algebras and their Casimir invariants
Umbral calculus, difference equations and the discrete Schrödinger equation
Lie symmetries and exact solutions of first-order difference schemes
Equivalence classes and symmetries of the variable coefficient Kadomtsev-Petviashvili equation
Discrete matrix Riccati equations with superposition formulas
Integrable and superintegrable quantum systems in a magnetic field
Continuous symmetries of Lagrangians and exact solutions of discrete equations
Symmetries, Lagrangian formalism and integration of second order ordinary difference equations
Superintegrable systems in Darboux spaces
Weak transversality and partially invariant solutions
Lie symmetries and superintegrability in quantum mechanics
A superintegrable time-dependent system with Kac-Moody symmetry
Generalized Kadomtsev-Petviashvili equation with an infinite-dimensional symmetry algebra
Superintegrability with third-order integrals in quantum and classical mechanics
Lie point symmetries and commuting flows for equations on lattices
Separation of variables and subgroup bases on $n$-dimensional hyperboloids
Quantum superintegrability and exact solvability in $n$ dimensions
Superintegrability in a two-dimensional space of nonconstant curvature
Derivation of Graf's addition theorem by contractions of the group $\rm SO(3)$
Lie symmetries of multidimensional difference equations
Invariants of the nilpotent and solvable triangular Lie algebras
Symmetries of the discrete nonlinear Schrödinger equation
Group foliation and non-invariant solutions of the heavenly equation
Symmetry classification of diatomic molecular chains
Exact solvability of superintegrable systems
Recursion operators, higher-order symmetries and superintegrability in quantum mechanics
Continuous symmetries of equations on lattices
Relation between Bäcklund transformations and higher continuous symmetries of the Toda equation
Time-dependent realization of the infinite-dimensional hydrogen algebra
Contractions of Lie algebras and the separation of variables: interbase expansions
Superintegrable systems in quantum mechanics and classical Lie theory
Lie point symmetries of difference equations and lattices
Invariant solutions of hydrodynamic-type equations
Point symmetries of generalized Toda field theories. II. Symmetry reduction
Bases for representations of quantum algebras
Lie point symmetry preserving discretizations for variable coefficient Korteweg-de Vries equations
Lie algebra contractions and symmetries of the Toda hierarchy
Discrete systems related to some equations of the Painlevé-Gambier classification
Huygens' principle and separation of variables
Integrable and superintegrable Hamiltonian systems in magnetic fields
Point symmetries of generalized Toda field theories
Lie group classification of second-order ordinary difference equations
Solutions of nonlinear differential and difference equations with superposition formulas
Singularity analysis, balance equations and soliton solution of the nonlocal complex Ginzburg-Landau equation
Nonlinear superposition formulas based on imprimitive group action
Symmetries of discrete dynamical systems involving two species
Symmetries of the discrete Burgers equation
Maximal abelian subalgebras of $e(p,q)$ algebras
Group invariant solutions for the $N=2$ super Korteweg-de-Vries equation
Contractions of Lie algebras and separation of variables. The $n$-dimensional sphere
Graded contractions of the Lie algebra $e(2,1)$
Lie group contractions and separation of variables
Discretizing families of linearizable equations
Solvable Lie algebras with triangular nilradicals
Solutions of $(2+1)$-dimensional spin systems
Maximal abelian subgroups of the isometry and conformal groups of Euclidean and Minkowski spaces
$P_\infty$ algebra of KP, free fermions and $2$-cocycle in the Lie algebra of pseudodifferential operators
$P_\infty$-algebra of symmetries of the Kadomtsev-Petviashvili equations, free fermions and $2$-cocycles in the Lie algebra of pseudodifferential operators
Lie-theoretical generalization and discretization of the Pinney equation
Symmetries and solutions of the vector nonlinear Schrödinger equation
Algebra of pseudodifferential operators and symmetries of equations in the Kadomtsev-Petviashvili hierarchy
Successive refinements of gradings and graded contractions of ${\rm sl}(3,{\bf C})$
Contractions of Lie algebras and separation of variables. Two-dimensional hyperboloid
Lie group formalism for difference equations
Grading refinements in the contractions of Lie algebras and their invariants
Contractions of Lie algebras and separation of variables
Symmetries of discrete dynamical systems
The conformal group ${\rm SU}(2,2)$ and integrable systems on a Lorentzian hyperboloid
Superposition formulas for pseudounitary matrix Riccati equations
On the solutions of the ${\bf C}{\rm P}^1$ model in $(2+1)$ dimensions
Classical and quantum integrable systems in $\widetilde{\germ g\germ l}(2)^{+*}$ and separation of variables
Harmonics on hyperspheres, separation of variables and the Bethe ansatz
Maximal abelian subalgebras of complex Euclidean Lie algebras
Generalized Casimir operators of solvable Lie algebras with abelian nilradicals
Solvable Lie algebras with abelian nilradicals
Symmetries and conditional symmetries of a nonrelativistic Chern-Simons system
Symmetry analysis of the Infeld-Rowlands equation
Symmetry classes of variable coefficient nonlinear Schrödinger equations
Representations of the quantum algebra ${\rm su}_q(2)$ on a real two-dimensional sphere
On the relation between weak and strong invariance of differential equations
Integrable systems based on ${\rm SU}(p,q)$ homogeneous manifolds
Symmetries and conditional symmetries of differential-difference equations
On the symmetry groups of the intrinsic generalized wave and sine-Gordon equations
Group theory and solutions of classical field theories with polynomial nonlinearities
Solvable Lie algebras with Heisenberg ideals
Evolution equations invariant under two-dimensional space-time Schrödinger group
Symmetries of variable coefficient Korteweg-de-Vries equations
Partially invariant solutions of a class of nonlinear Schrödinger equations
Allowed transformations and symmetry classes of variable coefficient Korteweg-de-Vries equations
Partially invariant solutions of nonlinear Klein-Gordon and Laplace equations
Maximal abelian subalgebras of pseudo-orthogonal Lie algebras
Exact solutions of the stimulated-Raman-scattering equations
Symmetry properties and solutions of nonlinear dispersive thin-film equations in three dimensions
The computer calculation of Lie point symmetries of large systems of differential equations
Graded contractions of ${\rm sl}(3,{\bf C})$
Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation
Continuous symmetries of discrete equations
Group theoretical analysis of dispersive long wave equations in two space dimensions
Maximal abelian subalgebras of complex orthogonal Lie algebras
Periodicity and quasi-periodicity for super-integrable Hamiltonian systems
Superposition formulas for nonlinear superequations
Point symmetries of conditionally integrable nonlinear evolution equations
Maximal abelian subalgebras of pseudounitary Lie algebras
Nonlinear equations invariant under the Poincaré, similitude, and conformal groups in two-dimensional space-time
Symmetries of semiclassical gravity in two dimensions
Analysis and applications of the symmetry group of the multidimensional three-wave resonant interaction problem
Group theoretical analysis of a rotating shallow liquid in a rigid container
Nonclassical symmetry reduction: example of the Boussinesq equation
Solitons in shallow seas of variable depth and in marine straits
Symmetries of the self-dual Einstein equations. I. The infinite-dimensional symmetry group and its low-dimensional subgroups
Lie symmetries of a generalised nonlinear Schrödinger equation. III. Reductions to third-order ordinary differential equations
Lie symmetries of a generalised nonlinear Schrödinger equation. II. Exact solutions
Exact solutions of the cubic and quintic nonlinear Schrödinger equation for a cylindrical geometry
Exact solutions of the spherical quintic nonlinear Schrödinger equation
Nonlinear equations with superposition formulas and exceptional group $G_2$. III. The superposition formulas
On the identification of a Lie algebra given by its structure constants. I. Direct decompositions, Levi decompositions, and nilradicals
Lie algebras under constraints and nonbijective canonical transformations
Lie symmetries of a generalised nonlinear Schrödinger equation. I. The symmetry group and its subgroups
The cylindrical Kadomtsev-Petviashvili equation: its Kac-Moody-Virasoro algebra and relation to KP equation
Equations invariant under the symmetry group of the Kadomtsev-Petviashvili equation
The classification of complete sets of operators commuting with the Dirac operator in Minkowski space-time
On the infinite-dimensional symmetry group of the Davey-Stewartson equations
Integrable nonlinear equations for water waves in straits of varying depth and width
Dynamical invariance algebra of the Hartmann potential
PASCAL programs for the identification of Lie algebras. II. SPLIT---a program to decompose parameter-free and parameter-dependent Lie algebras into direct sums
Exact solutions of the multidimensional classical $\phi^6$-field equations obtained by symmetry reduction
Nonlinear differential equations and Lie superalgebras
Superposition formulas for the rectangular matrix Riccati equations
Nonlinear equations with superposition formulas and the exceptional group $G_2$. II. Classification of the equations
New classes of exact solutions of the $\phi^6$ model in $3+1$ dimensions
ODEPAINLEVE---a MACSYMA package for Painlevé analysis of ordinary differential equations
Bäcklund transformations and the infinite-dimensional symmetry group of the Kadomtsev-Petviashvili equation
Are all the equations of the Kadomtsev-Petviashvili hierarchy integrable?
Nonlinear equations with superposition formulas and the exceptional group $G_2$. I. Complex and real forms of $g_2$ and their maximal subalgebras
On the integrability and perturbations of systems of ODEs with nonlinear superposition principles
Symmetry reduction for the Kadomtsev-Petviashvili equation using a loop algebra
On the integrability of systems of nonlinear ordinary differential equations with superposition principles
Complex parabolic subgroups of $G_2$ and nonlinear differential equations
Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles
Integrable Hamiltonian systems with velocity-dependent potentials
Subalgebras of loop algebras and symmetries of the Kadomtsev-Petviashvili equation
Abelian integrals and the reduction method for an integrable Hamiltonian system
Superposition laws for solutions of differential matrix Riccati equations arising in control theory
Separation of variables for the Hamilton-Jacobi equation on complex projective spaces
Nonlinear superposition principles: a new numerical method for solving matrix Riccati equations
Classification of systems of nonlinear ordinary differential equations with superposition principles
Comments on superposition rules for nonlinear coupled first-order differential equations
Symmetry reduction for nonlinear relativistically invariant equations
Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras
Maximal abelian subalgebras of real and complex symplectic Lie algebras
Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces
Normal forms of elements of classical real and complex Lie and Jordan algebras
Superposition principles for matrix Riccati equations
Solutions of the multidimensional sine-Gordon equation obtained by symmetry reduction
Pseudopotentials and Lie symmetries for the generalized nonlinear Schrödinger equation
Systems of ordinary differential equations with nonlinear superposition principles
Group theoretical approach to superposition rules for systems of Riccati equations
Subgroups of Lie groups and separation of variables
On the maximal abelian subgroups of the linear classical algebraic groups
On the maximal abelian subgroups of the quadratic classical algebraic groups
Discrete two-variable expansions of scattering amplitudes for particles with spin
Quadratic Hamiltonians in phase space and their eigenstates
Polynomial irreducible tensors for point groups
Sous-algèbres de Lie de l'algèbre de Schrödinger
Tensor fields invariant under subgroups of the conformal group of space-time
The optical group and its subgroups
Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups
Subalgebras of real three- and four-dimensional Lie algebras
Symmetry breaking interactions for the time dependent Schrödinger equation
On bases for irreducible representations of $O(3)$ suitable for systems with an arbitrary finite symmetry group
The group ${\rm O}(4)$, separation of variables and the hydrogen atom
Subgroups of the Poincaré group and their invariants
Quantum numbers for particles in de Sitter space
Subgroups of the similitude group of three-dimensional Minkowski space
Invariants of real low dimension Lie algebras
Canonical transformation and accidental degeneracy. III. A unified approach to the problem
Everything you always wanted to know about $SU(3)\supset {\rm O}(3)$
Continuous subgroups of the fundamental groups of physics. II. The similitude group
Continuous subgroups of the fundamental groups of physics. I. General method and the Poincaré group
Nagel-Moshinsky operators for discrete unitary representations of ${\rm U}(p, q)$
Complete sets of commuting operators and $O(3)$ scalars in the enveloping algebra of $S{\rm U}(3)$
The maximal solvable subgroups of ${\rm SO}(p,\,q)$ groups
The maximal solvable subgroups of the ${\rm SU}(p,\,q)$ groups and all subgroups of ${\rm SU}(2,\,1)$
Potential scattering and Galilei-invariant expansions of scattering amplitudes
Two-variable Galilei-group expansions of nonrelativistic scattering amplitudes
Invariant trilinear couplings involving both ${\rm SU}(2)$ and ${\rm SU}(1,\,1)$ states
One-parameter subgroups of unitary groups with indefinite metric and in particular of the conformal group
Crossing symmetric expansions of physical scattering amplitudes: the ${\rm O}(2,\,1)$ group and Lamé functions
Recursion and symmetry relations for the Clebsch-Gordan coefficients of the homogeneous Lorentz group
Clebsch-Gordan coefficients for the coupling of ${\rm SL}(2,\,C)$ principal-series representations
Representations of the Lorentz group: New integral relations between Legendre functions
Two-dimensional expansions of relativistic amplitudes in the Mandelstam triangle and crossing symmetric reactions
Symmetry groups in classical and quantum mechanics
On relativistic angular momentum theory
Invariant expansions of relativistic amplitudes and subgroups of the proper Lorentz group
On higher symmetries in quantum mechanics
The optical theorem for scattering of particles with arbitrary spins