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C. Scimiterna

Publications and source records attributed to C. Scimiterna.

7 recordsLinked to original sources
arXiv2015

Linearizability and fake Lax pair for a consistent around the cube nonlinear non-autonomous quad-graph equation

We discuss the linearization of a non-autonomous nonlinear partial difference equation belonging to the Boll classification of quad-graph equations consistent around the cube. We show that its Lax pair is fake. We present its generalized symmetries which turn out to be non-autonomous and depending on an arbitrary function of the dependent variables defined in two lattice points. These generalized symmetries are differential difference equations which, in some case, admit peculiar B\"acklund transformations.

nlin.SI↗
arXiv2013

High order multiscale analysis of discrete integrable equations

In this article we present the results obtained applying the multiple scale expansion up to the order $\varepsilon^6$ to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions given by the multiple scale expansion give rise to 4 nonlinear equations, 3 of which are new, depending at most on 2 parameters and containing integrable sub cases. Moreover at least one sub case provides an example of a new integrable system.

nlin.SI↗
arXiv2013

Four Points Linearizable Lattice Schemes

We provide conditions for a lattice scheme defined on a four points lattice to be linearizable by a point transformation. We apply the obtained conditions to a symmetry preserving difference scheme for the potential Burgers introduced by Dorodnitsyn \cite{db} and show that it is not linearizable.

nlin.SI↗
arXiv2010

A discrete linearizability test based on multiscale analysis

In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A_1, A_2 and A_3 linearizability conditions restrain the number of the parameters which enter into the equation. A subclass of the equations which pass the A_3 C-integrability conditions can be linearized by a Mobius transformation.

nlin.SI↗
arXiv2010

Integrability of Differential-Difference Equations with Discrete Kinks

In this article we discuss a series of models introduced by Barashenkov, Oxtoby and Pelinovsky to describe some discrete approximations to the \phi^4 theory which preserve travelling kink solutions. We show, by applying the multiple scale test that they have some integrability properties as they pass the A_1 and A_2 conditions. However they are not integrable as they fail the A_3 conditions.

nlin.SI↗
arXiv2009

Multiscale reduction of discrete nonlinear Schroedinger equations

We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability conditions for two well-known discretizations of the nonlinear Schroedinger equation.

math-ph↗