Integrability test for evolutionary lattice equations of higher order

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}.

💡 Research Summary

The paper addresses the problem of testing integrability for scalar evolutionary lattice equations of the form
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