Conference: Symbolic Computation of Lax Pairs of Nonlinear Systems of Partial Difference Equations using Multidimensional Consistency

Symbolic Computation of Lax Pairs of Systems of Nonlinear Partial Difference
Equations and Their Gauge Equivalence

Prof. Willy Hereman
Department of Applied Mathematics and Statistics
Colorado School of Mines
Golden, Colorado, U.S.A. home/whereman/

Martes 28 de Noviembre  16:00h


A method due to Nijhoff and Bobenko & Suris to derive Lax pairs for nonlinear systems of partial difference equations will be presented.

The systems featured in the talk are defined on a quadrilateral. They are multidimensional consistent but contain equations defined on the edges of the quadrilateral. It will be shown how the edge equations should be handled to obtain gauge-equivalent Lax matrices of minimal size.

Lax pairs will be presented for a two-component potential Korteweg-de Vries lattice system, as well as nonlinear Schrodinger and Boussinesq-type lattice systems. Such systems can be viewed as fully discrete versions of  well-known completely integrable partial differential equations from soliton theory.

The method to find Lax pairs of nonlinear partial difference equations is algorithmic and is being implemented in Mathematica. A demo of the software will be given.