Integrability Test for Discrete Equations via Generalized Symmetries

AIP Conference Proceedings 10/2010; 1323. DOI: 10.1063/1.3537849
Source: arXiv


In this article we present some integrability conditions for partial
difference equations obtained using the formal symmetries approach. We apply
them to find integrable partial difference equations contained in a class of
equations obtained by the multiple scale analysis of the general multilinear
dispersive difference equation defined on the square.

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    • "Fortunately, more arguments do exist. First, Levi and Yamilov [10] have shown that (2) with c 2 = 1/2 admits a five-point generalized symmetry, a property usually associated with integrability. Moreover Viallet [11] has computed the algebraic entropy [12] of both systems and shown that it is zero, which constitutes another indication of integrability. "
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