Integrable discrete autonomous quad-equations admitting,as generalized symmetries,known five-point differential-difference equations |
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| Authors: | Rustem N Garifullin Ravil I Yamilov |
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| Institution: | 1. Institute of Mathematics, Ufa Federal Research Centre, Russian Academy of Sciences, 112 Chernyshevsky Street, Ufa 450008, Russian Federation rustem@matem.anrb.ru;2. Institute of Mathematics, Ufa Federal Research Centre, Russian Academy of Sciences, 112 Chernyshevsky Street, Ufa 450008, Russian Federation RvlYamilov@matem.anrb.ru |
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| Abstract: | In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to autonomous point transformations and some simple non-autonomous transformations. We discuss our results in the framework of the known literature. There are among them a few new examples of both sine-Gordon and Liouville type equations. |
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| Keywords: | Integrability Generalized symmetries Quad-equations |
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