61 citations · 332 across the 19 of their papers we have counts for
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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…
Darboux transformations with tetrahedral reduction group and related integrable systems
George Berkeley, Alexander V. Mikhailov, Pavlos Xenitidis
In this paper we derive new two-component integrable differential difference and partial difference systems by applying a Lax-Darboux scheme to an operator formed from an ${\mathfr…
graded discrete Lax pairs and Yang-Baxter maps
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 this paper we introduce…
Reduction groups and related integrable difference systems of NLS type
S. Konstantinou-Rizos, A. V. Mikhailov, P. Xenitidis
We extend the reduction group method to the Lax-Darboux schemes associated with nonlinear Schrödinger type equations. We consider all possible finite reduction groups and construct…
graded discrete Lax pairs and discrete integrable systems
Allan P. Fordy, Pavlos Xenitidis
We introduce a class of graded discrete Lax pairs, with matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs…
Second order integrability conditions for difference equations. An integrable equation
Alexandre V. Mikhailov, Pavlos Xenitidis
Integrability conditions for difference equations admitting a second order formal recursion operator are presented and the derivation of symmetries and canonical conservation laws…
Lattice Schwarzian Boussinesq equation and two-component systems
Pavlos Xenitidis, Frank Nijhoff
Various new two-component systems related to the lattice Schwarzian Boussinesq equation are constructed in a systematic way from conservation laws. Their multidimensional consisten…
Symmetries and conservation laws of lattice Boussinesq equations
Pavlos Xenitidis, Frank Nijhoff
Sequences of canonical conservation laws and generalized symmetries for the lattice Boussinesq and the lattice modified Boussinesq systems are successively derived. The interpretat…
Symmetry algebra of discrete KdV equations and corresponding differential-difference equations of Volterra type
Pavlos Xenitidis
A sequence of canonical conservation laws for all the Adler-Bobenko-Suris equations is derived and is employed in the construction of a hierarchy of master symmetries for equations…
Cosymmetries and Nijenhuis recursion operators for difference equations
Alexander V. Mikhailov, Jing Ping Wang, Pavlos Xenitidis
In this paper we discuss the concept of cosymmetries and co--recursion operators for difference equations and present a co--recursion operator for the Viallet equation. We also dis…
On the Lagrangian formulation of multidimensionally consistent systems
Pavlos Xenitidis, Frank Nijhoff, Sarah Lobb
Multidimensional consistency has emerged as a key integrability property for partial difference equations (PEs) defined on the "space-time" lattice. It has led, among other majo…
Recursion operators, conservation laws and integrability conditions for difference equations
Alexander V. Mikhailov, Jing Ping Wang, Pavlos Xenitidis
In this paper we make an attempt to give a consistent background and definitions suitable for the theory of integrable difference equations. We adapt a concept of recursion operato…
Symmetries and integrability of discrete equations defined on a black-white lattice
P. D. Xenitidis, V. G. Papageorgiou
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,…
Integrability and Symmetries of Difference Equations: the Adler-Bobenko-Suris Case
P. Xenitidis
We consider the partial difference equations of the Adler-Bobenko-Suris classification, which are characterized as multidimensionally consistent. The latter property leads naturall…
Affine linear and D4 symmetric lattice equations : symmetry analysis and reductions
A. Tongas, D. Tsoubelis, P. Xenitidis
We consider lattice equations on ${\mathds{Z}}^2$ which are autonomous, affine linear and possess the symmetries of the square. Some basic properties of equations of this type are…