Inverse scattering and soliton dynamics for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation

Abstract

Under investigation in this letter is a mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation which can be considered as the simplest model to approximate the dynamics of weakly nonlinear and dispersive waves, taking into account the self-steepening effect. The inverse scattering transform under the zero boundary conditions and analytical scattering coefficients with an arbitrary number of simple and double zeros is detailedly discussed. Particularly, the inverse problem is solved by the study of a matrix Riemann–Hilbert problem. As a consequence, we present the general solution for the potential, and explicit expression for the reflectionless potential.