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Classification of discrete systems on a square lattice
R. Hernandez Herederoa, D. Levib, Ch. Scimiternab a 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.
Citation:
R. Hernandez Heredero, D. Levi, Ch. Scimiterna, “Classification of discrete systems on a square lattice”, TMF, 172:2 (2012), 250–263; Theoret. and Math. Phys., 172:2 (2012), 1097–1108
Linking options:
https://www.mathnet.ru/eng/tmf6954https://doi.org/10.4213/tmf6954 https://www.mathnet.ru/eng/tmf/v172/i2/p250
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Abstract page: | 315 | Full-text PDF : | 152 | References: | 66 | First page: | 12 |
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