Multi-Soliton Solutions for the Coupled Fokas-Lenells System via Riemann-Hilbert Approach

We aim to construct multi-soliton solutions for the coupled Fokas-Lenells system which arises as a model for describing the nonlinear pulse propagation in optical fibers. Starting from the spectral analysis of the Lax pair, a Riemann-Hilbert problem is presented. Then in the framework of the Riemann-Hilbert problem corresponding to the reflectionless case, N-soliton solutions to the coupled Fokas-Lenells system are derived explicitly.