Integrability test for evolutionary lattice equations of higher order

Abstract

A generalized summation by parts algorithm is presented for solving of difference equations of the form $T^m(y)-a[u]y=b[u]$ where $T$ denotes the shift $u_j\to u_{j+1}$. Solvability of such type of equations with respect to coefficients of formal symmetry (or formal recursion operator) provides a convenient integrability test for evolutionary differential-difference equations $u_{,t}=f(u_{-m},\dots ,u_m)$. The algorithm is implemented in {\em Mathematica}.

22 pages

References in corpus (4)

• Classification of integrable polynomial vector evolution equations
• Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I
• Integrable evolution equations with constant separant
• Necessary integrability conditions for evolutionary lattice equations

Cited by in corpus (4)

• Classification of five-point differential-difference equations
• Classification of five-point differential-difference equations II
• Integrable Möbius invariant evolutionary lattices of second order
• Non-invertible transformations for the classification of differential-difference equations