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arXiv · 1711.02516

A Riemann-Hilbert Approach to the Kundu-Eckhaus Equation on the half-Line

Beibei Hu·Tiecheng Xia·Ning Zhang
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Abstract

In this paper, we consider the initial-boundary value problem of the Kundu-Eckhaus equation on the half-line by using of the Fokas unified transform method. Assuming that the solution $u(x,t)$ exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter $\lambda$. Moreover, we also get there exist spectral functions are not independent and they are satisfying the so-called global relation.

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Beibei Hu, Tiecheng Xia, Ning Zhang. 2017-11-04. A Riemann-Hilbert Approach to the Kundu-Eckhaus Equation on the half-Line. https://arxiv.org/abs/1711.02516

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