Caudrelier, V (2015) On the Inverse Scattering Method for Integrable PDEs on a Star Graph. Communications in Mathematical Physics, 338 (2). pp. 893-917. ISSN 0010-3616
Abstract
We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then to extend the unified method of Fokas to such a matrix IBV problem. The nonlinear Schrödinger equation is chosen to illustrate the method. The framework unifies all previously known examples which are recovered as particular cases. The case of general Robin conditions at the vertex is discussed: the notion of linearizable initial-boundary conditions is introduced. For such conditions, the method is shown to be as efficient as the ISM on the full-line.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2015, Springer Verlag. This is an author produced version of a paper published in Communications in Mathematical Physics. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via https://doi.org/10.1007/s00220-015-2378-9 |
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: | 14 Feb 2017 12:03 |
Last Modified: | 20 Jan 2018 06:20 |
Published Version: | https://doi.org/10.1007/s00220-015-2378-9 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00220-015-2378-9 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:108996 |