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On the degenerate soliton solutions of the focusing nonlinear Schrödinger equation
Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260 – USA.
Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260 – USA.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics. Uniwersytet Jana Kochanowskiego Kielcach, Inst Matemat, Kielcach, Poland.
2017 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 58, no 3, 033507Article in journal (Other academic) Published
Abstract [en]

We characterize the N-soliton solutions of the focusing nonlinear Schrodinger (NLS) equation with degenerate velocities, i.e., solutions in which two or more soliton velocities are the same, which are obtained when two or more discrete eigenvalues of the scattering problem have the same real parts. We do so by employing the operator formalism developed by one of the authors to express the N-soliton solution of the NLS equation in a convenient form. First we analyze soliton solutions with fully degenerate velocities (a so-called multi-soliton group), clarifying their dependence on the soliton parameters. We then consider the dynamics of soliton groups interaction in a general N-soliton solution. We compute the long-time asymptotics of the solution and we quantify the interaction-induced position and phase shifts of each non-degenerate soliton as well as the interaction-induced changes in the center of mass and soliton parameters of each soliton group.

Place, publisher, year, edition, pages
2017. Vol. 58, no 3, 033507
Keyword [en]
Solitons, Nonlinear Schrodinger equation, Inverse scattering, Long-time asymptotics
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-29468DOI: 10.1063/1.4977984ISI: 000397873800036Scopus ID: 2-s2.0-85016255505OAI: oai:DiVA.org:miun-29468DiVA: diva2:1052894
Available from: 2016-12-07 Created: 2016-12-07 Last updated: 2017-04-25Bibliographically approved

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Schiebold, Cornelia

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CiteExportLink to record
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Citation style
  • apa
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  • de-DE
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  • en-US
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  • nn-NO
  • nn-NB
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