报告题目: |
Integrability of difference equations |
报告人: |
Prof. Alexander V. Mikhailov |
|
Department of Applied Mathematics , University of Leeds, UK
|
报告时间: |
2010-11-02 16:00 |
报告地点: |
理科楼1304报告厅 |
主办单位: |
数学科学系 |
简介: |
We set up an algebraic framework for difference equations their symmetries and conservation laws. With a difference equation we associate a prime difference ideal and the difference field of fractions. Then symmetries and conservation laws can be regarded as exceptional properties of the field. Existence of symmetries, or more precisely, of a formal recursion operator is taken as a definition of integrability. We have constructed an infinite sequence of integrability conditions for a given difference equation which are necessary conditions for the existence of a formal recursion operator. These conditions are presented in the form of a canonical sequence of conservation laws for a difference equation. We have found a recursion operator suitable for all equations from the Adler-Bobenko-Suris classification. This operator is a composition of a Hamiltonian and symplectic operators which equip the ABS equations with a multi-Hamiltonian structure. This recursion operator has also a remarkable factorization over the field of fractions defined by the difference equation. Also I am planning to discuss the concepts of co-symmetries and co-recursion operators, if time permits. |
|
