Backlund transformations for integrable lattice equations

Abstract

We give new Backlund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of two other kinds. Specifically, it is found that some equations admit additional auto-BTs (with Backlund parameter), whilst some pairs of apparently distinct equations admit a BT which connects them.

9 pages

References in corpus (3)

• Classification of integrable equations on quad-graphs. The consistency approach
• Bäcklund transformation for the Krichever-Novikov equation
• A new two-dimensional lattice model that is "consistent around a cube"

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• Linear quadrilateral lattice equations and multidimensional consistency
• Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method
• Infinitely many conservation laws for the discrete KdV equation
• Continuous symmetric reductions of the Adler-Bobenko-Suris equations
• Extended Z-invariance for integrable vector and face models and multi-component integrable quad equations
• Integrability of auto-Bäcklund transformations,and solutions of a torqued ABS equation
• A Revisit to the ABS H2 Equation
• Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation