Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 1, October 2019, Pages 130 - 161

Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations with Mixed Sign Reductions and Nonzero Boundary Conditions

Authors
Alyssa K. Ortiz1
1Department of Mathematics, University of Colorado Colorado Springs, 1420 Austin Bluffs Pkwy Colorado Springs, Colorado 80918, United States,aortiz@uccs.edu,bprinari@uccs.edu
Barbara Prinari1, 2
2Department of Mathematics, University of Buffalo, 244 Mathematics Building Buffalo, New York 14260, United States,bprinari@buffalo.edu
Received 1 March 2019, Accepted 13 July 2019, Available Online 25 October 2019.
DOI
10.1080/14029251.2020.1683996How to use a DOI?
Keywords
Inverse scattering transform; nonlinear waves; solitons; nonlinear Schrödinger systems
Abstract

The inverse scattering transform (IST) with nonzero boundary conditions at infinity is developed for a class of 2 × 2 matrix nonlinear Schrödinger-type systems whose reductions include two equations that model certain hyperfine spin F = 1 spinor Bose-Einstein condensates, and two novel equations that were recently shown to be integrable, and that have applications in nonlinear optics and four-component fermionic condensates. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows us to develop the IST on the standard complex plane instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity, symmetries and asymptotics of the scattering eigenfunctions and scattering data are derived, and properties of the discrete spectrum are analyzed in detail. In addition, the general behavior of the soliton solutions for all four reductions is discussed, and some novel soliton solutions are presented.

Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
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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<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 1
Pages
130 - 161
Publication Date
2019/10/25
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1683996How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
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  - Alyssa K. Ortiz
AU  - Barbara Prinari
PY  - 2019
DA  - 2019/10/25
TI  - Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations with Mixed Sign Reductions and Nonzero Boundary Conditions
JO  - Journal of Nonlinear Mathematical Physics
SP  - 130
EP  - 161
VL  - 27
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1683996
DO  - 10.1080/14029251.2020.1683996
ID  - Ortiz2019
ER  -