224 citations · 2.5k across the 74 of their papers we have counts for
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Lie point symmetries and ODEs passing the Painlevé test
Decio Levi, David Sekera, Pavel Winternitz
The Lie point symmetries of ordinary differential equations (ODEs) that are candidates for having the Painlevé property are explored for ODEs of order . Among the 6…
Conformally invariant elliptic Liouville equation and its symmetry preserving discretization
Decio Levi, Luigi Martina, Pavel Winternitz
The symmetry algebra of the real elliptic Liouville equation is an infinite-dimensional loop algebra with the simple Lie algebra as its maximal finite-dimensional subalgeb…
Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests
Decio Levi, Luigi Martina, Pavel Winternitz
The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Thre…
Lie group analysis of a generalized Krichever-Novikov differential-difference equation
Decio Levi, Eugenio Ricca, Zora Thomova +1
The symmetry algebra of the differential--difference equation where , and are…
First integrals of ordinary difference equations beyond Lagrangian methods
V. Dorodnitsyn, E. Kaptsov, R. Kozlov +1
A new method for finding first integrals of discrete equations is presented. It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) fo…
Continuous Symmetries of Difference Equations
D. Levi, P. Winternitz
Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much m…
Lie Symmetries and Exact Solutions of First Order Difference Schemes
Miguel A. Rodriguez, Pavel Winternitz
We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In gener…
Symmetries of Discrete Systems
Pavel Winternitz
In this series of lectures presented at the CIMPA Winter School on Discrete Integrable Systems in Pondicherry, India, in February, 2003 we give a review of the application of Lie p…
Continuous symmetries of Lagrangians and exact solutions of discrete equations
Vladimir Dorodnitsyn, Roman Kozlov, Pavel Winternitz
One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei inva…
Umbral Calculus, Difference Equations and the Discrete Schroedinger Equation
Decio Levi, Piergiulio Tempesta, Pavel Winternitz
We discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The m…
Symmetry Classification of Diatomic Molecular Chains
S. Lafortune, S. Tremblay, P. Winternitz
A symmetry classification of possible interactions in a diatomic molecular chain is provided. For nonlinear interactions the group of Lie point transformations, leaving the lattice…
Generalized Kadomtsev-Petviashvili equation with an infinite dimensional symmetry algebra
F. Gungor, P. Winternitz
A generalized Kadomtsev-Petviashvili equation, describing water waves in oceans of varying depth, density and vorticity is discussed. A priori, it involves 9 arbitrary functions of…
Point Symmetries of Generalized Toda Field Theories II Applications of the Symmetries
L. Martina, S. Lafortune, P. Winternitz
The Lie symmetries of a large class of generalized Toda field theories are studied and used to perform symmetry reduction. Reductions lead to generalized Toda lattices on one hand,…
Point Symmetries of Generalized Toda Field Theories
S. Lafortune, P. Winternitz, L. Martina
A class of two-dimensional field theories with exponential interactions is introduced. The interaction depends on two ``coupling'' matrices and is sufficiently general to include a…