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Entwining Yang-Baxter maps related to NLS type equations

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arxiv 1907.00019 v1 pith:OD5GI6HM submitted 2019-06-28 nlin.SI math-phmath.MP

S. Konstantinou-Rizos , G. Papamikos This is my paper · ORCID
classification nlin.SImath-phmath.MP
keywords mapsassociateddarbouxentwiningequationsrelatedtypeyang-baxter
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We construct birational maps that satisfy the parametric set-theoretical Yang-Baxter equation and its entwining generalisation. For this purpose, we employ Darboux transformations related to integrable Nonlinear Schr\"odinger type equations and study the refactorisation problems of the product of their associated Darboux matrices. Additionally, we study various algebraic properties of the derived maps, such as invariants and associated symplectic or Poisson structures, and we prove their complete integrability in the Liouville sense.

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  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.

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