Darboux transformations, finite reduction groups and related Yang-Baxter maps
Abstract
In this paper we construct Yang-Baxter (YB) maps using Darboux matrices which are invariant under the action of finite reduction groups. We present 6-dimensional YB maps corresponding to Darboux transformations for the Nonlinear Schr\"odinger (NLS) equation and the derivative Nonlinear Schr\"odinger (DNLS) equation. These YB maps can be restricted to dimensional YB maps on invariant leaves. The former are completely integrable and they also have applications to a recent theory of maps preserving functions with symmetries \cite{Allan-Pavlos}. We give a dimensional YB-map corresponding to the Darboux transformation for a deformation of the DNLS equation. We also consider vector generalisations of the YB maps corresponding to the NLS and DNLS equation.
Cite
@article{arxiv.1205.4910,
title = {Darboux transformations, finite reduction groups and related Yang-Baxter maps},
author = {Sotiris Konstantinou-Rizos and Alexander Mikhailov},
journal= {arXiv preprint arXiv:1205.4910},
year = {2015}
}
Comments
18 pages, revised version. The format of the paper has changed, we added one section