Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 41, Issue -, Pages 334-361Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2017.10.014
Keywords
Kundu-Eckhaus equation; Riemann-Hilbert approach; Lax pair; Long-time asymptotics; Soliton solutions
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Funding
- National Natural Science Foundation of China [11375030, 11472315, 11401031]
- Beijing Finance Funds of Natural Science Program for Excellent Talents [2014000026833ZK19]
- Qin Xin Talents Cultivation Program of Beijing Information Science and Technology University [QXTCP B201704, QXTCP A201702]
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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. (C) 2017 Elsevier Ltd. All rights reserved.
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