Classification of evolutionary equations on the lattice. I. The general theory

Abstract

A modification of the symmetry approach for the classification of integrable differential-difference equations of the form $$u_{n,t}=f_n(u_{n-1},u_n,u_{n+1}),$$ where $n$ is a discrete integer variable, is presented (the well-known Volterra and Toda equations can be written in this form). If before, in the framework of the symmetry approach, only equations similar to $$u_{n,t}=f(u_{n-1},u_n,u_{n+1}),$$ i.e. defined by a function $f$, were considered, now we have an infinite set $f_n$ of a priori quite different functions.

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Cited by in corpus (3)

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• A non autonomous generalization of the $Q_{\text{V}}$ equation