Inverse scattering transforms for non-local reverse-space matrix non-linear Schrödinger equations

The aim of the paper is to explore non-local reverse-space matrix non-linear Schrödinger equations and their inverse scattering transforms. Riemann–Hilbert problems are formulated to analyse the inverse scattering problems, and the Sokhotski–Plemelj formula is used to determine Gelfand–Levitan–March...

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Bibliographic Details
Published inEuropean journal of applied mathematics Vol. 33; no. 6; pp. 1062 - 1082
Main Authors MA, WEN-XIU, HUANG, YEHUI, WANG, FUDONG
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 01.12.2022
Subjects
Applied mathematics
Integral equations
Inverse scattering
Mathematical analysis
Schrodinger equation
Solitary waves
Transformations (mathematics)
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Summary:The aim of the paper is to explore non-local reverse-space matrix non-linear Schrödinger equations and their inverse scattering transforms. Riemann–Hilbert problems are formulated to analyse the inverse scattering problems, and the Sokhotski–Plemelj formula is used to determine Gelfand–Levitan–Marchenko-type integral equations for generalised matrix Jost solutions. Soliton solutions are constructed through the reflectionless transforms associated with poles of the Riemann–Hilbert problems.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792521000334