Geodesic
Classification of discrete systems on a~square lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 2, pp. 250-263

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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.
Mots-clés : multiscale expansion
Keywords: difference equation, integrable model, linearizable model. 
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     author = {R. Hernandez Heredero and D. Levi and Ch. Scimiterna},
     title = {Classification of discrete systems on a~square lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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R. Hernandez Heredero; D. Levi; Ch. Scimiterna. Classification of discrete systems on a~square lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 2, pp. 250-263. http://geodesic.mathdoc.fr/item/TMF_2012_172_2_a5/