High-order semi-rational solutions of the coupled nonlinear Schrödinger equations with variable coefficients

Abstract

In this paper, we consider coupled variable coefficients nonlinear Schrödinger equations (VCNLS), which can be used to describe the interaction among the modes in nonlinear optics and Bose–Einstein condensation. With the help of a gauge transformation of the spectral problem, the generalized Darboux transformation (DT) for the VCNLS is constructed. As an application of the generalized DT, we first derive the second-order and third-order semi-rational solutions of the VCNLS. In addition, we investigate the dynamics of the second-order and third-order semi-rational solutions with different coefficients. Finally we find that the coefficients [Formula: see text] and [Formula: see text] mainly affect the shape of the above solutions, while the amplification or absorption coefficient [Formula: see text] will change the amplitude. The obtained results will enrich the study of theory of the nonlinear localized waves.