Whitham modulation theory and Riemann problem for the Kundu-Eckhaus equation

被引:1
作者
Tan, QingShan [1 ]
Zhang, Jian [1 ]
机构
[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China
基金
中国国家自然科学基金;
关键词
Kundu-Eckhaus equation; Periodic solutions; Finite-gap integration method; Whitham modulation theory; Riemann problem; NONLINEAR SCHRODINGER-EQUATION; LONG-TIME ASYMPTOTICS; PERIODIC-SOLUTIONS; SHOCK-WAVES; SYSTEMS; EVOLUTION; NLS;
D O I
10.1016/j.physd.2024.134380
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, the Riemann problem for the defocusing Kundu-Eckhaus equation is investigated by Whitham modulation theory. First, we study the dispersion relation for linear waves. Then, the zero-phase and one- phase periodic solutions of the Kundu-Eckhaus equation along with the corresponding Whitham modulation equations are derived by the finite-gap integration method. Further, employing the Whitham equations parametrized by the Riemann invariants, the main fundamental wave structures induced by the discontinuous initial data are found. Analytical and graphic methods are utilized to provide the wave structures of rarefaction waves and dispersive shock waves, and thus for a complete classification of solutions under general step-like conditions of initial discontinuity.
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页数:12
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