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

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

1995-11-16

arxiv.org/abs/solv-int/9511006v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages, AmsTeX

Scientific paper

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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