Generalized Darboux transformation and parameter-dependent rogue wave solutions to a nonlinear Schrödinger system

Abstract

In this work, we are concerned with a generalized nonlinear Schrodinger equation, which can describe the propagation of nonlinear wave phenomena in plasma, optics and in deep water field. We construct, up to the second-order expansion, rogue wave solutions and give general formula to obtain higher-order ones to this system. We investigate the effects of the higher-order nonlinearity on the rogue waves dynamics. We make use of the generalized Darboux transformation, based on the Darboux matrix method.