Display Abstract

Title Integrable systems via conservation laws

Name Peter Hydon
Country England
Email P.Hydon@surrey.ac.uk
Co-Author(s) Claude-M. Viallet
Submit Time 2010-02-16 10:31:41
Special Session 66: Discrete Integrable Systems
Integrable difference equations commonly have more low-order conservation laws than occur for nonintegrable difference equations of similar complexity. We use this empirical observation to sift a large class of difference equations, in order to find candidates for integrability. The candidates can all be written in affine linear form, so we have tested their integrability by calculating their algebraic entropy. In this way, we have found several integrable equations, none of which are in the Adler-Bobenko-Suris classifications. Indeed, one of the equations seems to be entirely new. A useful by-product of this method is a complete classification of single-tile conservation laws.