Generalized symmetry classification of discrete equations of a class depending on twelve parameters

Details Generalized symmetry classification of discrete equations of a class depending on twelve parameters Generalized symmetry classification of discrete equations of a class depending on twelve parameters

2012-03-20

arxiv.org/abs/1203.4369v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

submitted to J. Phys. A: Math. Theor

Scientific paper

We carry out the generalized symmetry classification of polylinear autonomous discrete equations defined on the square, which belong to a twelve-parametric class. As a result we find a number of integrable examples pretending to be new. One of them has a nonstandard symmetry structure, the others are analogues of the Liouville equation in the sense that those are Darboux integrable. We also enumerate all equations of the class, which are linearizable via a two-point first integral, and specify the nature of integrability of some known equations.

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