Bury, R, Mikhailov, AV and Wang, JP (2017) Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system. Physica D: Nonlinear Phenomena, 347. pp. 21-41. ISSN 0167-2789
Abstract
In the paper we develop the dressing method for the solution of the two-dimensional periodic Volterra system with a period N. We derive soliton solutions of arbitrary rank k and give a full classification of rank 1 solutions. We have found a new class of exact solutions corresponding to wave fronts which represent smooth interfaces between two nonlinear periodic waves or a periodic wave and a trivial (zero) solution. The wave fronts are non-stationary and they propagate with a constant average velocity. The system also has soliton solutions similar to breathers, which resembles soliton webs in the KP theory. We associate the classification of soliton solutions with the Schubert decomposition of the Grassmannians GrR(k,N) and GrC(k,N).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY). |
Keywords: | High rank solitons; The KP equation; Two dimensional Volterra system; Dressing method; Wave front solutions; Reduction group |
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: | 26 Jan 2017 12:32 |
Last Modified: | 01 Nov 2017 13:21 |
Published Version: | https://doi.org/10.1016/j.physd.2017.01.003 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.physd.2017.01.003 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111203 |
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