Caudrelier, V and Zhang, QC (2014) Yang–Baxter and reflection maps from vector solitons with a boundary. Nonlinearity, 27. pp. 1081-1103. ISSN 0951-7715
Abstract
Based on recent results obtained by the authors on the inverse scatteringmethod of the vector nonlinear Schr\ödinger equation with integrable boundaryconditions, we discuss the factorization of the interactions of N-solitonsolutions on the half-line. Using dressing transformations combined with amirror image technique, factorization of soliton-soliton and soliton-boundaryinteractions is proved. We discover a new object, which we call reflection map,that satisfies a set-theoretical reflection equation which we also introduce.Two classes of solutions for the reflection map are constructed. Finally, basicaspects of the theory of set-theoretical reflection equations are introduced.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 IOP Publishing Ltd & London Mathematical Society. This is an author-created, un-copyedited version of an article published in Nonlinearity. OP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/0951-7715/27/6/1081. |
Keywords: | Yang–Baxter maps, reflection maps, vector nonlinear Schr ̈ odinger equation, boundary, dressing method |
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: | 07 Sep 2017 14:27 |
Last Modified: | 15 Jan 2018 19:14 |
Published Version: | http://arxiv.org/abs/1205.1133v3 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/0951-7715/27/6/1081 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:109005 |