Speaker: Pavlos Xenitidis (Liverpool Hope University, UK)
Date and time: 07.04.2021, 17:00 (GMT +03:00)
Title: Symmetries and Integrability of Difference Equations
Abstract: Symmetries provide arguably the most reliable means to test and prove the integrability of a given equation. They are used in the analysis and classification of partial differential equations and differential-difference equations since 1970’s and 1980’s, and only very recently this approach has been extended to partial difference equations. In this talk I will consider a class of partial difference equations in two dimensions and discuss the general form of their symmetries. I will derive necessary integrability conditions for these equations and explain how they lead to symmetries and conservation laws. I will also demonstrate how symmetries can be used to find solutions and reduce a partial difference equation to discrete Painlevé type equations. Finally, I will discuss several extensions of the theory to other classes of scalar equations and to systems of difference equations.
To access the online seminar please contact Anna Tolbey firstname.lastname@example.org