Article

Integrability Test for Discrete Equations via Generalized Symmetries

10/2010;
Source: arXiv

ABSTRACT In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations contained in a class of equations obtained by the multiple scale analysis of the general multilinear dispersive difference equation defined on the square. Comment: Proceedings of the Symposium in Memoriam Marcos Moshinsky

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    ABSTRACT: We examine two lattice equations, obtained through the application of multiscale perturbative analysis, from the point of view of integrability. We show that both equations are integrable and related to the discrete sine-Gordon. We compute the limit of both systems whereby they become linearizable, obtaining the discrete Liouville equation and a linearizable lattice system recently proposed by Hydon and Viallet. We present the explicit solution of the latter.
    Journal of Physics A Mathematical and Theoretical 12/2010; 44(3):032002. · 1.77 Impact Factor

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