Initial-boundary value problem and long-time asymptotics for the Kundu--Eckhaus equation on the half-line

Boling Guo; Nan Liu

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arXiv · 1712.03821

Initial-boundary value problem and long-time asymptotics for the Kundu--Eckhaus equation on the half-line

Boling Guo·Nan Liu

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Abstract

The initial-boundary value problem for the Kundu--Eckhaus equation on the half-line is considered in this paper by using the Fokas method. We will show that the solution $u(x,t)$ can be expressed in terms of the solution of a matrix Riemann--Hilbert problem formulated in the complex $k$-plane. Furthermore, based on a nonlinear steepest descent analysis of the associated Riemann--Hilbert problem, we can give the precise asymptotic formulas for the solution of the Kundu--Eckhaus equation on the half-line.

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Boling Guo, Nan Liu. 2017-12-08. Initial-boundary value problem and long-time asymptotics for the Kundu--Eckhaus equation on the half-line. https://arxiv.org/abs/1712.03821

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