Imaginary eigenvalues of Zakharov–Shabat problems with non-zero background

Gino Biondini; Xudan Luo

doi:10.1016/j.physleta.2018.06.045

Imaginary eigenvalues of Zakharov–Shabat problems with non-zero background

Gino Biondini
, Xudan Luo

Mathematics

SUNY Buffalo

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The focusing Zakharov–Shabat scattering problem on the infinite line with non-zero boundary conditions for the potential is studied, and sufficient conditions on the potential are identified to ensure that the problem admits only purely imaginary discrete eigenvalues. The results, which generalize previous work by Klaus and Shaw, are applicable to the study of solutions of the focusing nonlinear Schrödinger equation with non-zero background.

Original language	English
Pages (from-to)	2632-2637
Number of pages	6
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	382
Issue number	37
DOIs	https://doi.org/10.1016/j.physleta.2018.06.045
State	Published - Sep 22 2018

Keywords

Discrete eigenvalues
Inverse scattering
Nonlinear Schrödinger equation
Zakharov–Shabat scattering problem

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10.1016/j.physleta.2018.06.045

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title = "Imaginary eigenvalues of Zakharov{\textendash}Shabat problems with non-zero background",

abstract = "The focusing Zakharov{\textendash}Shabat scattering problem on the infinite line with non-zero boundary conditions for the potential is studied, and sufficient conditions on the potential are identified to ensure that the problem admits only purely imaginary discrete eigenvalues. The results, which generalize previous work by Klaus and Shaw, are applicable to the study of solutions of the focusing nonlinear Schr{\"o}dinger equation with non-zero background.",

keywords = "Discrete eigenvalues, Inverse scattering, Nonlinear Schr{\"o}dinger equation, Zakharov{\textendash}Shabat scattering problem",

author = "Gino Biondini and Xudan Luo",

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year = "2018",

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T1 - Imaginary eigenvalues of Zakharov–Shabat problems with non-zero background

AU - Biondini, Gino

AU - Luo, Xudan

PY - 2018/9/22

Y1 - 2018/9/22

N2 - The focusing Zakharov–Shabat scattering problem on the infinite line with non-zero boundary conditions for the potential is studied, and sufficient conditions on the potential are identified to ensure that the problem admits only purely imaginary discrete eigenvalues. The results, which generalize previous work by Klaus and Shaw, are applicable to the study of solutions of the focusing nonlinear Schrödinger equation with non-zero background.

AB - The focusing Zakharov–Shabat scattering problem on the infinite line with non-zero boundary conditions for the potential is studied, and sufficient conditions on the potential are identified to ensure that the problem admits only purely imaginary discrete eigenvalues. The results, which generalize previous work by Klaus and Shaw, are applicable to the study of solutions of the focusing nonlinear Schrödinger equation with non-zero background.

KW - Discrete eigenvalues

KW - Inverse scattering

KW - Nonlinear Schrödinger equation

KW - Zakharov–Shabat scattering problem

UR - https://www.scopus.com/pages/publications/85049581862

U2 - 10.1016/j.physleta.2018.06.045

DO - 10.1016/j.physleta.2018.06.045

M3 - Article

AN - SCOPUS:85049581862

SN - 0375-9601

VL - 382

SP - 2632

EP - 2637

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 37

ER -

Imaginary eigenvalues of Zakharov–Shabat problems with non-zero background

Abstract

Keywords

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