Families of Integrable Equations

Abstract

We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3-parameters and their members are connected through Bäcklund transformations. At least one of the members of each family is integrable, hence the whole family inherits some integrability properties.

References in corpus (4)

• Classification of 3D consistent quad-equations
• On Quadrirational Yang-Baxter Maps
• On non-multiaffine consistent-around-the-cube lattice equations
• A higher-rank version of the Q3 equation

Cited by in corpus (12)

• Tetrahedron maps and symmetries of three dimensional integrable discrete equations
• Invariants in Separated Variables: Yang-Baxter, Entwining and Transfer Maps
• Yang--Baxter maps, Darboux transformations, and linear approximations of refactorisation problems
• Idempotent biquadratics, Yang-Baxter maps and birational representations of Coxeter groups
• Difference systems in bond and face variables and non-potential versions of discrete integrable systems
• Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
• Tetrahedron maps, Yang-Baxter maps, and partial linearisations
• Systems of difference equations on a vector valued function that admit 3D space of scalar potentials
• Multi-quadratic quad equations: integrable cases from a factorised-discriminant hypothesis
• Discrete Lax pairs and hierarchies of integrable difference systems
• Integrable multi-component difference systems of equations
• $2^n-$rational maps