Caudrelier, V orcid.org/0000-0003-0129-6758, Crampé, N, Ragoucy, E et al. (1 more author) (2023) Nonlinear Schrödinger equation on the half-line without a conserved number of solitons. Physica D: Nonlinear Phenomena, 445. 133650. ISSN 0167-2789
Abstract
We explore the phenomena of absorption/emission of solitons by an integrable boundary for the focusing nonlinear Schrödinger equation on the half-line. This is based on the investigation of time-dependent reflection matrices which satisfy the boundary zero curvature equation. In particular, this leads to absorption/emission processes at the boundary that can take place for solitons and higher-order solitons. As a consequence, the usual charges on the half-line are no longer conserved but we show explicitly how to restore an infinite set of conserved quantities by taking the boundary into account. The Hamiltonian description and Poisson structure of the model are presented, which allows us to derive for the first time a classical version of the boundary algebra used originally in the context of the quantum nonlinear Schrödinger equation.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 Elsevier B.V. All rights reserved. This is an author produced version of an article published in Physica D: Nonlinear Phenomena. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse scattering method; Time-dependent integrable boundary conditions; Soliton solutions on the half-line; Classical boundary algebra |
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: | 20 Jan 2023 15:24 |
Last Modified: | 10 Jan 2024 01:13 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.physd.2023.133650 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:195392 |