On a nonlinear integrable difference equation on the square 3D-inconsistent

Details On a nonlinear integrable difference equation on the square 3D-inconsistent On a nonlinear integrable difference equation on the square 3D-inconsistent

2009-02-12

arxiv.org/abs/0902.2126v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

We present a nonlinear partial difference equation defined on a square which is obtained by combining the Miura transformations between the Volterra and the modified Volterra differential-difference equations. This equation is not symmetric with respect to the exchange of the two discrete variables and does not satisfy the 3D-consistency condition necessary to belong to the Adler-Bobenko-Suris classification. Its integrability is proved by constructing its Lax pair.

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