Integrable discrete nonautonomous quad-equations as B?cklund auto-transformations for known Volterra and Toda type semidiscrete equations

7th International Workshop: Group Analysis of Differential Equations and Integrable Systems

Garifullin, Rustem N.^1 ; Yamilov, Ravil I.^1

Ufa Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky Street, Ufa

450008, Russia^1

关键词: Conservation law;    Discrete equations;    General solutions;    Liouville;    Nonautonomous;    Semi-discrete equations;    Sine-Gordon-type equations;    Volterra;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012005/pdf
DOI  :  10.1088/1742-6596/621/1/012005

来源: IOP

【 摘 要 】

We construct integrable discrete nonautonomous quad-equations as Bäcklund autotransformations for known Volterra and Toda type semidiscrete equations, some of which are also nonautonomous. Additional examples of this kind are found by using transformations of discrete equations which are invertible on their solutions. In this way we obtain integrable examples of different types: discrete analogs of the sine-Gordon equation, the Liouville equation and the dressing chain of Shabat. For Liouville type equations we construct general solutions, using a specific linearization. For sine-Gordon type equations we find generalized symmetries, conservation laws and L - A pairs.