Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation

Under investigation in this paper is a coupled nonlinear Schrödinger (NLS) equation, which describes nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order. Based on the Lax pair of the coupled NLS equation, we construct the determinant representation of the N-fold Darboux transformation(DT). Furthermore, by using the obtained N-fold DT, we obtain its higher-order soliton, breather and rogue wave solutions. Finally, the dynamic characteristics of these solutions are discussed.