On non-multiaffine consistent-around-the-cube lattice equations

Abstract

We show that integrable involutive maps, due to the fact they admit three integrals in separated form, can give rise to equations, which are consistent around the cube and which are not in the multiaffine form assumed in papers [1, 2]. Lattice models, which are discussed here, are related to the lattice potential KdV equation by nonlocal transformations (discrete quadratures).

Isaac Newton Institute for Mathematical Sciences Preprint No NI11010-DIS 2011

References in corpus (6)

• An Inverse Scattering Transform for the Lattice Potential KdV Equation
• On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
• Backlund transformations for integrable lattice equations
• The staircase method: integrals for periodic reductions of integrable lattice equations
• A multidimensionally consistent version of Hirota's discrete KdV equation
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• A noncommutative discrete potential KdV lift
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• Families of Integrable Equations
• Invariants in Separated Variables: Yang-Baxter, Entwining and Transfer Maps
• A multidimensionally consistent version of Hirota's discrete KdV equation
• On the $3D$ consistency of a Grassmann extended lattice Boussinesq system
• Entwining Yang-Baxter maps related to NLS type equations
• 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
• Algebraic and differential-geometric constructions of set-theoretical solutions to the Zamolodchikov tetrahedron equation
• Local Yang--Baxter correspondences and set-theoretical solutions to the Zamolodchikov tetrahedron equation
• Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
• Birational solutions to the set-theoretical 4-simplex equation
• Tetrahedron maps, Yang-Baxter maps, and partial linearisations
• Multi-quadratic quad equations: integrable cases from a factorised-discriminant hypothesis
• Discrete Lax pairs and hierarchies of integrable difference systems
• Systems of difference equations on a vector valued function that admit 3D space of scalar potentials
• Darboux transformations, discrete integrable systems and related Yang-Baxter maps
• Integrable multi-component difference systems of equations
• Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems
• $2^n-$rational maps