Long-time asymptotics and the bright N-soliton solutions of the Kundu–Eckhaus equation via the Riemann–Hilbert approach

The long-time asymptotics and bright N-soliton solutions of the Kundu–Eckhaus equation are studied by Riemann–Hilbert approach. Firstly, the initial value problem of the defocusing Kundu–Eckhaus equation is considered and its long-time asymptotics is derived based on the nonlinear steepest descent m...

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Published inNonlinear analysis: real world applications Vol. 41; pp. 334 - 361
Main Authors Wang, Deng-Shan, Wang, Xiaoli
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Ltd 01.06.2018
Elsevier BV
Subjects
Asymptotic methods
Asymptotic properties
Boundary value problems
Defocusing
Kundu–Eckhaus equation
Lax pair
Long-time asymptotics
Nonlinear equations
Riemann–Hilbert approach
Schrodinger equation
Soliton solutions
Steepest descent method
Long-time asymptotics
Soliton solutions
Lax pair
Kundu–Eckhaus equation
Riemann–Hilbert approach
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Summary:The long-time asymptotics and bright N-soliton solutions of the Kundu–Eckhaus equation are studied by Riemann–Hilbert approach. Firstly, the initial value problem of the defocusing Kundu–Eckhaus equation is considered and its long-time asymptotics is derived based on the nonlinear steepest descent method of Deift–Zhou. Then the linear spectral problem of the focusing Kundu–Eckhaus equation is investigated via Riemann–Hilbert formulation and the bright N-soliton solutions of this equation are obtained explicitly.
Bibliography:ObjectType-Article-1
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ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2017.10.014