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

2017/12/08 by Guo, Boling, Liu, Nan
#Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.1712.03821

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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