Nonlinear Schrödinger type tetrahedron maps

2020/05/27 by Sotiris Konstantinou-Rizos, Konstantinou-Rizos, Sotiris · 2 citations
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.2005.13574

19 pages, 3 figures. The main steps of the proposed method are now formulated into a scheme. The part concerning the integrability of the derived maps will appear in another text, where the integrability of the derived maps is studied from various aspects

arxiv created 2020/08/05 · arxiv updated 2022/03/01

Abstract

This paper is concerned with the construction of new solutions in terms of birational maps to the functional tetrahedron equation and parametric tetrahedron equation. We present a method for constructing solutions to the parametric tetrahedron equation via Darboux transformations. In particular, we study matrix refactorisation problems for Darboux transformations associated with the nonlinear Schrödinger (NLS) and the derivative nonlinear Schrödinger (DNLS) equation, and we construct novel nine-dimensional tetrahedron maps. We show that the latter can be restricted to six-dimensional parametric tetrahedron maps on invariant leaves. Finally, we construct parametric tetrahedron maps employing degenerated Darboux transformations of NLS and DNLS type.

Cited by

• Noncommutative NLS systems: Darboux--Bäcklund transformations and integrable discretisations
• From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations

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