Darboux transformation with Dihedral reduction group

Abstract

We construct the Darboux transformation with Dihedral reduction group for the 2-dimensional generalisation of the periodic Volterra lattice. The resulting Backlund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry. Using formal diagonalisation of the Darboux matrix we obtain local conservation laws of the system.

References in corpus (4)

• Darboux transformations and Recursion operators for differential--difference equations
• Integrability and Symmetries of Difference Equations: the Adler-Bobenko-Suris Case
• Reduction groups and related integrable difference systems of NLS type
• Automorphic Lie Algebras with dihedral symmetry

Cited by in corpus (9)

• Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere
• Reduction groups and related integrable difference systems of NLS type
• Formal diagonalisation of Lax-Darboux schemes
• Higher dimensional Automorphic Lie Algebras
• Automorphic Lie Algebras with dihedral symmetry
• Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system
• Representations of sl(2,C) in the BGG category O and master symmetries
• Invariants of Automorphic Lie Algebras
• Discrete integrable systems, Darboux transformations, and Yang-Baxter maps