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 in | Nonlinear analysis: real world applications Vol. 41; pp. 334 - 361 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Amsterdam
Elsevier Ltd
01.06.2018
Elsevier BV |
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| Abstract | 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. |
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| AbstractList | The long-time asymptotics and bright N-soliton solutions of the Kundu-Eckhaus equation are studied by R.iemann-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. 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. |
| Author | Wang, Deng-Shan Wang, Xiaoli |
| Author_xml | – sequence: 1 givenname: Deng-Shan surname: Wang fullname: Wang, Deng-Shan email: wangdsh1980@163.com organization: School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China – sequence: 2 givenname: Xiaoli surname: Wang fullname: Wang, Xiaoli organization: School of Science, Qilu University of Technology, Daxue Road, Jinan, 250353, China |
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| Snippet | The long-time asymptotics and bright N-soliton solutions of the Kundu–Eckhaus equation are studied by Riemann–Hilbert approach. Firstly, the initial value... The long-time asymptotics and bright N-soliton solutions of the Kundu-Eckhaus equation are studied by R.iemann-Hilbert approach. Firstly, the initial value... |
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| SubjectTerms | 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 |
| Title | Long-time asymptotics and the bright N-soliton solutions of the Kundu–Eckhaus equation via the Riemann–Hilbert approach |
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