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

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 $\lambda$. Thus, the solution $\{q(x,t),r(x,t)\}$ can be obtained by integration with respect to $x$.

18 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1704.03623

References in corpus (3)

• On a novel integrable generalization of the nonlinear Schrödinger equation
• A Riemann-Hilbert Approach to the Kundu-Eckhaus Equation on the half-Line
• Long-time asymptotics for initial-boundary value problems of integrable Fokas-Lenells equation on the half-line

Cited by in corpus (1)

• An initial-boundary value problem for the coupled focusing-defocusing complex short pulse equation with a $4\times 4$ Lax pair