Classification of discrete systems on a square lattice

R. Hernandez Heredero^a, D. Levi^b, Ch. Scimiterna<sup>b

a</sup> Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, Escuela Universitaria de Ingeniería Técnica de Telecomunicación, Madrid, Spain
^b Dipartimento di Ingegneria Elettronica, Università degli Studi Roma Treand Sezione INFN, Roma Tre, Rome, Italy

Abstract: We consider the classification up to a Möbius transformation of real linearizable and integrable partial difference equations with dispersion defined on a square lattice by the multiscale reduction around their harmonic solution. We show that the $A_1$, $A_2$, and $A_3$ linearizability and integrability conditions constrain the number of parameters in the equation, but these conditions are insufficient for a complete characterization of the subclass of multilinear equations on a square lattice.

Keywords: multiscale expansion, difference equation, integrable model, linearizable model.

DOI: 10.4213/tmf6954

 English version: Theoretical and Mathematical Physics, 2012, 172:2, 1097–1108

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