Riemann–Hilbert method and multi-soliton solutions for three-component coupled nonlinear Schrödinger equations

An integrable three-component coupled nonlinear Schrödinger (NLS) equation is considered in this work. We present the scattering and inverse scattering problems of the three-component coupled NLS equation by using the Riemann–Hilbert formulation. Furthermore, according to the Riemann–Hilbert method, the multi-soliton solutions of this equation are derived. We also analyze the collision dynamic behaviors of these solitons. Moreover, a new phenomenon for two-soliton collision is displayed, which is unique and not common in integrable systems. It is hoped that our results can help enrich the nonlinear dynamics of the NLS-type equations.