This first introductory text to discrete integrable systems introduces key notions of
integrability from the vantage point of discrete systems, also making connections with the …

We consider the partial difference equations of the Adler-Bobenko-Suris classification, which
are characterized as multidimensionally consistent. The latter property leads naturally to the …

A Lie system is a system of differential equations admitting a superposition rule, ie, a
function describing its general solution in terms of any generic set of particular solutions and …

The main relationship between the anti-self-dual Yang–Mills equations (ASDYM) and
integrable systems of partial differential equations (PDEs) stems from the fact that most well …

This work represents a PhD thesis concerning three main topics. The first one deals with the
study and applications of Lie systems with compatible geometric structures, eg symplectic …

In this paper, under the Painlevé-integrable condition, the auto-Bäcklund transformations in
different forms for a variable-coefficient Korteweg-de Vries model with physical interests are …

Continuously symmetric solutions of the Adler–Bobenko–Suris class of discrete integrable
equations are presented. Initially defined by their invariance under the action of both of the …

On a fairly imprecise, first approximation, the universal definition of integrability is
understood as the exact solvability or regular behavior of solutions of a system …

We show how to construct four-dimensional anti-self-dual conformal structures from
solutions of a parameter family of partial differential equations which generalize the Ernst …