Lie point symmetries of differential--difference equations

TL;DR

This paper introduces an algorithm to find Lie point symmetries of differential-difference equations on fixed lattices, with applications to integrable models like the Toda lattice and Krichever-Novikov equation.

Contribution

The paper develops a general method for computing Lie point symmetries of mixed continuous-discrete equations and applies it to notable integrable systems.

Findings

Successfully applied the algorithm to the Toda lattice and Toda field theory.

Identified symmetries of the Krichever-Novikov equation.

Provides a systematic approach for symmetry analysis of differential-difference equations.

Abstract

We present an algorithm for determining the Lie point symmetries of differential equations on fixed non transforming lattices, i.e. equations involving both continuous and discrete independent variables. The symmetries of a specific integrable discretization of the Krichever-Novikov equation, the Toda lattice and Toda field theory are presented as examples of the general method.