Dark soliton solutions for a coupled nonlinear Schrödinger system

Under investigation in this paper is the coupled nonlinear Schrödinger system which describes the mode-locked fiber lasers. Based on the Hirota method and Kadomtsev–Petviashvili hierarchy reduction method, N-dark–dark soliton solutions are derived. Features and asymptotic behaviors of dark–dark solitons are analyzed in detail, and typical dynamics has been demonstrated. Both proportional and not proportional single dark–dark solitons in u and v components are studied. Interactions of two dark–dark solitons are demonstrated. We find that there is no energy transfer between the two solitons or between the u and v components before and after the interactions.