DIS

Abstract

The talk focuses on scalar 2-dimensional nonlinear partial difference equations (P-Delta-Es) which are completely integrable, i.e., they admit a Lax representation.

Based on work by Nijhoff, Bobenko and Suris, a method to compute Lax pairs will be presented. The method is largely algorithmic and can be implemented in the syntax of computer algebra systems, such as Mathematica and Maple.

A Mathematica program will be demonstrated that automatically computes Lax pairs for a variety of P-Delta-Es on quad-graphs, including lattice versions of the potential Korteweg-de Vries (KdV) equations, the modified KdV and sine-Gordon equations, as well as lattices derived by Adler, Bobenko, and Suris.

The symbolic computation of Lax pairs of nonlinear systems of integrable P-Delta-Es is work in progress. A few initial examples will be shown.