Konstantinou-Rizos, S and Mikhailov, A (2012) Darboux transformations, finite reduction groups and related Yang-Baxter maps. Journal of Physics A: Mathematical and Theoretical, 46 (425201). ? - ? (16). ISSN 1751-8113
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 $4-$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 $6-$ 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 28 Mar 2014 12:35 |
Last Modified: | 02 May 2015 01:04 |
Published Version: | http://iopscience.iop.org/1751-8121/46/42/425201/p... |
Status: | Published |
Publisher: | IOP Pubishing |
Identification Number: | 10.1088/1751-8113/46/42/425201 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:76136 |