Journal of Nonlinear Mathematical Physics

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Volume 28, Issue 1, March 2021, Pages 68 - 89

Focusing NLS Equations with Nonzero Boundary Conditions: Triangular Representations and Direct Scattering

Authors
Cornelis van der Mee*
Dip. Matematica e Informatica, Universit’a di Cagliari, Via Ospedale 72, Cagliari 09124, Italy
Corresponding Author
Cornelis van der Mee
Received 10 December 2019, Accepted 6 May 2020, Available Online 10 December 2020.
DOI
10.2991/jnmp.k.200922.006How to use a DOI?
Keywords
AKNS system; triangular representation
Abstract

In this article we derive the triangular representations of the fundamental eigensolutions of the focusing 1 + 1 AKNS system with symmetric nonvanishing boundary conditions. Its continuous spectrum equals 𝕉∪[-iμ,iμ] , where μ is the absolute value of the AKNS solution at spatial infinity. We also study the behavior of the scattering coefficients near the endpoints ±iμ of the branch cut, where we distinguish between the generic case and the exceptional case.

Copyright
© 2020 The Author. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
28 - 1
Pages
68 - 89
Publication Date
2020/12/10
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.k.200922.006How to use a DOI?
Copyright
© 2020 The Author. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Cornelis van der Mee
PY  - 2020
DA  - 2020/12/10
TI  - Focusing NLS Equations with Nonzero Boundary Conditions: Triangular Representations and Direct Scattering
JO  - Journal of Nonlinear Mathematical Physics
SP  - 68
EP  - 89
VL  - 28
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.200922.006
DO  - 10.2991/jnmp.k.200922.006
ID  - vanderMee2020
ER  -