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

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arxiv 1106.0435 v2 pith:3PI5Y4KZ submitted 2011-06-01 nlin.SI math-phmath.MP

Pavlos Kassotakis , Maciej Nieszporski This is my paper · ORCID
classification nlin.SImath-phmath.MP
keywords latticeequationsformadmitaroundassumedconsistentconsistent-around-the-cube
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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).

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Integrable multi-component difference systems of equations

    nlin.SI 2019-08 conditional novelty 7.0 of 10

    Two new families of integrable multi-component difference systems in bond variables are constructed, with Lax pairs, Yang-Baxter maps, and reductions to the ABS quad-equations.

  2. Idempotent compatible maps and discrete integrable systems on the triangular lattice

    nlin.SI 2025-04 conditional novelty 6.0 of 10

    Three new families of idempotent, non-invertible compatible maps yield Yang-Baxter companion maps and integrable difference equations on the triangular lattice.

  3. Non-Abelian elastic collisions, associated difference systems of equations and discrete analytic functions

    nlin.SI 2024-12 conditional novelty 6.0 of 10

    A single non-abelian system of equations unifies classical and relativistic elastic collisions, and its lattice reinterpretation subsumes both the linear and nonlinear theories of discrete analytic functions.

  4. Systems of difference equations on a vector valued function that admit 3D space of scalar potentials

    nlin.SI 2019-08 conditional novelty 6.0 of 10

    For known involutive maps on CP1 times CP1, the paper exhaustively lists the 3D space of separated-variable invariants and uses them to derive vertex potentials, recovering the ABS list of integrable difference equations.

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