Group Analysis of Differential Equations and Integrable Systems − 2018
Pavlos Xenitidis (School of Mathematics, Statistics & Actuarial Science, University of Kent, UK)
Deautonomization of integrable difference equations
Abstract:
Integrability conditions for difference equations can be used not only to check the integrability of a given equation but also to compute its generalised symmetries and derive conservation laws. In this talk we explore one more application of these conditions: the construction of integrable nonautonomous equations. We demonstrate how the integrability conditions can be used to deautonomize a given autonomous equation and apply this procedure to a certain family of equations defined on an elementary quadrilateral of the ${\mathbb{Z}}^2$ lattice. In particular we show that all the nonautonomous equations we find are related via Miura transformations to the same integrable twoquad autonomous equation. Finally we prove the integrability of the latter equation by generating an infinite hierarchy of its symmetries using a local master symmetry.
