The coupled Fokas-Lenells equations by a Riemann-Hilbert approach

2017/11/09 by Beibei Hu, Hu, Beibei, Tiecheng Xia +1
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Topics in Algebra #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1711.03861

Abstract

In this paper, we use the unified transform method to consider the initial-boundary value problem for the coupled Fokas-Lenells equations on the half-line, assuming that the solution \q(x,t),r(x,t)\ of the coupled Fokas-Lenells equations exists, we show that \q_x(x,t),r_x(x,t)\ can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ. Thus, the solution \q(x,t),r(x,t)\ can be obtained by integration with respect to x.

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