61 citations · 332 across the 19 of their papers we have counts for
20 papers
Integrable discretisations of the noncommutative NLS equation
S. Konstantinou-Rizos, P. Xenitidis
We show how to derive noncommutative versions of integrable partial difference equations using Darboux transformations. As an illustrative example, we use the nonlinear Schrödinger…
Noncommutative discrete equations, symmetries and reductions
Pavlos Xenitidis
Employing the Lax pairs of the noncommutative discrete potential Korteweg--de Vries (KdV) and Hirota's KdV equations, we derive differential--difference equations that are consiste…
Systems of difference equations, symmetries and integrability conditions
Louis Brady, Pavlos Xenitidis
We consider a class of systems of difference equations defined on an elementary quadrilateral of the lattice, define their eliminable and dynamical variables, and…
A discrete Darboux-Lax scheme for integrable difference equations
Xenia Fisenko, Sotiris Konstantinou-Rizos, Pavlos Xenitidis
We propose a discrete Darboux-Lax scheme for deriving auto-Bäcklund transformations and constructing solutions to quad-graph equations that do not necessarily possess the 3D consis…
On consistent systems of difference equations
Pavlos Xenitidis
We consider overdetermined systems of difference equations for a single function which are consistent, and propose a general framework for their analysis. The integrability of…
Self-Dual Systems, their Symmetries and Reductions to the Bogoyavlensky Lattice
Allan P. Fordy, Pavlos Xenitidis
We recently introduced a class of graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In particular, we introduce…