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arXiv · 2011.13603

Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations

Rustem N. Garifullin·Ismagil T. Habibullin
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Abstract

In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable lattices admit two hierarchies of generalized symmetries corresponding to the discrete and continuous independent variables $n$ and $x$. Symmetries corresponding to the direction of $n$ are constructed in a more or less standard way while when constructing symmetries of the other form we meet a problem of solving a functional equation. We have shown that to handle with this equation one can effectively use the concept of characteristic Lie-Rinehart algebras of semi-discrete models. Based on this observation, we have proposed a classification method for integrable semi-discrete lattices. One of the interesting results of this work is a new example of an integrable equation, which is a semi-discrete analogue of the Tzizeica equation. Such examples were not previously known.

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Rustem N. Garifullin, Ismagil T. Habibullin. 2020-11-27. Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations. https://doi.org/10.1088/1751-8121%2Fabf3ea

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