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

2011/06/30 by Pavlos Kassotakis, Maciej Nieszporski · 2 citations
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.MP #msc:82B20 #msc:37K35 #msc:39A05

paper · pdf · doi:10.1016/j.physleta.2012.10.009

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

arxiv created 2011/09/30 · arxiv updated 2015/05/28

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).

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• From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations
• Idempotent compatible maps and discrete integrable systems on the triangular lattice

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