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arxiv: 1708.02456 · v1 · submitted 2017-08-08 · 🌊 nlin.SI

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Classification of five-point differential-difference equations II

R.N. Garifullin , R.I. Yamilov , D. Levi
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classification 🌊 nlin.SI
keywords equationsclassificationdifferential-differencefive-pointautonomousgeneralizedtransformationsarticle
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Using the generalized symmetry method we finish a classification, started in the article [R.N. Garifullin, R.I. Yamilov and D. Levi, Classification of five-point differential-difference equations, J. Phys. A: Math. Theor. 50 (2017) 125201 (27pp)], of integrable autonomous five-point differential-difference equations. The resulting list, up to autonomous point transformations, contains 14 equations some of which seem to be new. We have found non-autonomous or non-point transformations relating most of the obtained equations among themselves as well as their generalized symmetries.

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  1. On matrix Lax representations for (1+1)-dimensional evolutionary differential-difference equations

    nlin.SI 2026-04 unverdicted novelty 7.0

    General theory for gauge equivalence and simplification of matrix Lax pairs in evolutionary differential-difference equations, applied to construct new two-component integrable systems and Miura transformations.