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

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.

arXiv comment25 pages, 2 figures. arXiv admin note: text overlap with arXiv:1704.03456; text overlap with arXiv:1205.1559, arXiv:0808.1534 by other authors

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Cited by in corpus (3)

• Long-time asymptotics for the Hirota equation on the half-line
• The coupled Fokas-Lenells equations by a Riemann-Hilbert approach
• An initial-boundary value problem for the coupled focusing-defocusing complex short pulse equation with a $4\times 4$ Lax pair