Semi-rational solutions of N-coupled variable-coefficient nonlinear Schrödinger equation

In this paper, N ( N = 2 , 3 ⋯ ) coupled nonlinear Schrodinger equations with variable coefficients have been studied via the Darboux transformation, which have been used to describe the interaction among nonlinear optics and other interdisciplinary subjects. Higher-order semi-rational solutions have been attained. As an example, it has been discussed the propagation and interaction of rogue wave and soliton for the 3 coupled nonlinear Schrodinger equations with variable coefficients: one- and two-order solitons with rogue waves have been discussed.