Integrability test for evolutionary lattice equations of higher order. (May 2016) - Adler, V.E.
Abstract: A generalized summation by parts algorithm is presented for solving of difference equations of the form T m ( y ) − a y = b with variable coefficients, where T denotes the shift operator. Solvability of equations of this type with respect to the coefficients of formal symmetry (or formal recursion operator) provides a convenient integrability test for evolutionary differential-difference equations u, t = f ( u − m, …, u m ) .