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Long-time asymptotics and the bright \(N\)-soliton solutions of the Kundu-Eckhaus equation via the Riemann-Hilbert approach. (English) Zbl 1387.35056

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.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35Q15 Riemann-Hilbert problems in context of PDEs
35C08 Soliton solutions
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