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

D. Levi; R. I. Yamilov

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arXiv · 0902.2126

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

D. Levi·R. I. Yamilov

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Abstract

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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D. Levi, R. I. Yamilov. 2009-04-28. On a nonlinear integrable difference equation on the square 3D-inconsistent. https://arxiv.org/abs/0902.2126

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