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

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Levi, D.
Yamilov, R. I.
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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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Nonlinear Sciences - Exactly Solvable and Integrable Systems
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