Discrete integrable systems via conservation laws
- When?
- Wednesday 28 April 2010, 16:00 to 17:00
- Where?
- 24AA04
- Open to:
- Students, Staff
- Speaker:
- Professor Peter Hydon (Surrey)
Abstract: How can one discover a new integrable system? Various approaches have been used to answer this question for integrable PDEs, but relatively few integrable difference equations are known at present. We introduce an approach that is based on the following observation: for a given degree of complexity, integrable difference equations commonly have more low-order conservation laws than nonintegrable ones do. We have used this observation to sift a large class of difference equations, in order to find candidates for integrability.
Having constructed a shortlist, we tested the candidates' integrability by calculating their algebraic entropy. In this way, we have found several integrable equations, none of which are in the best-known class.
Indeed, one of the equations is entirely new, and recently it has led us to another new discrete integrable system.
A useful by-product of our method is a complete classification of low-order conservation laws; from these we have constructed an infinite hierarchy of conservation laws.
