Integrable Discrete Nonautonomous Quad-equations as Bäcklund Auto-transformations for Known Volterra and Toda Type Semidiscrete Equations

Abstract

We construct integrable discrete nonautonomous quad-equations as Bäcklund auto-transformations 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.

18 pages, submitted to Journal of Physics: Conference Series (JPCS)

References in corpus (5)

• Generalized symmetry integrability test for discrete equations on the square lattice
• Integrability and Symmetries of Difference Equations: the Adler-Bobenko-Suris Case
• On a discrete analog of the Tzitzeica equation
• On the integrability of a new lattice equation found by multiple scale analysis
• Examples of Darboux Integrable Discrete Equations Possessing First Integrals of an Arbitrarily High Minimal Order

Cited by in corpus (6)

• An unusual series of autonomous discrete integrable equations on the square lattice
• Asymptotic diagonalization of the Discrete Lax pair around singularities and conservation laws for dynamical systems
• Dressing the Dressing Chain
• Integrable Modifications of the Ito-Narita-Bogoyavlensky Equation
• Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation
• On a series of Darboux integrable discrete equations on the square lattice