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

2009/02/12 by D. Levi, Levi, D., R. I. Yamilov +1 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.0902.2126

openalex publication_date 2009/02/12 · arxiv created 2009/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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