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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 172, Number 2, Pages 250–263
DOI: https://doi.org/10.4213/tmf6954 (Mi tmf6954) 		 
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
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DOI: https://doi.org/10.4213/tmf6954
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.
English version:
Theoretical and Mathematical Physics, 2012, Volume 172, Issue 2, Pages 1097–1108
DOI: https://doi.org/10.1007/s11232-012-0098-2
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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