Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations *

Preface: Symmetries and Integrability of Difference Equations

Preface: Symmetries and Integrability of Difference Equations

Integrability conditions for nonautonomous quad-graph equations

This paper presents a systematic investigation of the integrability conditions for nonautonomous quad-graph maps, using the Lax pair approach, the ultra-local singularity confinement criterion and direct construction of conservation laws. We show that the integrability conditions derived from each of the methods are the one and the same, suggesting that there exists a deep connection between th...

Symmetries and integrability of discrete equations defined on a black–white lattice

We study the deformations of the H equations, presented recently by Adler, Bobenko and Suris, which are naturally defined on a black-white lattice. For each one of these equations, two different three-leg forms are constructed, leading to two different discrete Toda type equations. Their multidimensional consistency leads to Bäcklund transformations relating different members of this class, as ...

Four Lectures: Discretization and Integrability. Discrete Spectral Symmetries