Nonlinear Schr\"odinger type tetrahedron maps
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 Schr\"odinger (NLS) and the derivative nonlinear Schr\"odinger (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.
Keywords
Cite
@article{arxiv.2005.13574,
title = {Nonlinear Schr\"odinger type tetrahedron maps},
author = {Sotiris Konstantinou-Rizos},
journal= {arXiv preprint arXiv:2005.13574},
year = {2022}
}
Comments
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