Sun, Y-Y, Zhang, D-J and Nijhoff, FW (2017) The Sylvester equation and the elliptic Korteweg-de Vries system. Journal of Mathematical Physics, 58. 033504. ISSN 0022-2488
Abstract
The elliptic potential Korteweg-de Vries lattice system is a multi-component extension of the lattice potential Korteweg-de Vries equation, whose soliton solutions are associated with an elliptic Cauchy kernel (i.e., a Cauchy kernel on the torus). In this paper we generalize the class of solutions by allowing the spectral parameter to be a full matrix obeying a matrix version of the equation of the elliptic curve, and for the Cauchy matrix to be a solution of a Sylvester type matrix equation subject to this matrix elliptic curve equation. The construction involves solving the matrix elliptic curve equation by using Toeplitz matrix techniques, and analysing the solution of the Sylvester equation in terms of Jordan normal forms. Furthermore, we consider the continuum limit system associated with the elliptic potential Korteweg-de Vries system, and analyse the dynamics of the soliton solutions, which reveals some new features of the elliptic system in comparison to the non-elliptic case.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article is protected by copyright, all rights reserved. Published by AIP Publishing. Reproduced in accordance with the publisher's self-archiving policy. |
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: | 18 Jun 2018 10:49 |
Last Modified: | 23 Jun 2018 02:08 |
Status: | Published |
Publisher: | American Institute of Physics |
Identification Number: | 10.1063/1.4977477 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132157 |