Inverse Scattering Transform for Nonlinear Schrödinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions

Barbara Prinari

doi:10.1007/s44198-023-00120-w

Inverse Scattering Transform for Nonlinear Schrödinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions

Barbara Prinari

Mathematics

Research output: Contribution to journal › Review article › peer-review

10 Scopus citations

Abstract

In this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix NLS systems on the line (- ∞< x< ∞) with certain physically relevant non-zero boundary conditions at space infinity, discuss some new developments and applications, and offer some perspectives about future directions on the subject.

Original language	English
Pages (from-to)	317-383
Number of pages	67
Journal	Journal of Nonlinear Mathematical Physics
Volume	30
Issue number	2
DOIs	https://doi.org/10.1007/s44198-023-00120-w
State	Published - Jun 2023

Keywords

Integrable systems
Inverse scattering transform
Nonlinear Schrödinger systems
Solitons

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10.1007/s44198-023-00120-w

Cite this

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title = "Inverse Scattering Transform for Nonlinear Schr{\"o}dinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions",

abstract = "In this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix NLS systems on the line (- ∞< x< ∞) with certain physically relevant non-zero boundary conditions at space infinity, discuss some new developments and applications, and offer some perspectives about future directions on the subject.",

keywords = "Integrable systems, Inverse scattering transform, Nonlinear Schr{\"o}dinger systems, Solitons",

author = "Barbara Prinari",

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year = "2023",

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AU - Prinari, Barbara

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N2 - In this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix NLS systems on the line (- ∞< x< ∞) with certain physically relevant non-zero boundary conditions at space infinity, discuss some new developments and applications, and offer some perspectives about future directions on the subject.

AB - In this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix NLS systems on the line (- ∞< x< ∞) with certain physically relevant non-zero boundary conditions at space infinity, discuss some new developments and applications, and offer some perspectives about future directions on the subject.

KW - Integrable systems

KW - Inverse scattering transform

KW - Nonlinear Schrödinger systems

KW - Solitons

UR - https://www.scopus.com/pages/publications/85161631427

U2 - 10.1007/s44198-023-00120-w

DO - 10.1007/s44198-023-00120-w

M3 - Review article

AN - SCOPUS:85161631427

SN - 1402-9251

VL - 30

SP - 317

EP - 383

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

IS - 2

ER -

Inverse Scattering Transform for Nonlinear Schrödinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions

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Keywords

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