Continuous symmetries of difference equations

By D. Levi, P. Winternitz. 2005

137 citations recorded by the source corpus.

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 more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict them to point symmetries, but to allow them to also transform the lattice.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d6aa4c6af110a3c406e733488509352493122ffe

Citations in the corpus

• Symmetries of Integrable Difference Equations on the Quad‐Graph (2007, unknown): “An alternative approach to symmetries of difference equations (not only integrable ones) is to try to construct discretizations of differential equations that retain all Lie point symmetries of the original system [8, 18, 19].”