Darboux transformation and soliton-like solutions for the Gerdjikov-Ivanov equation

Abstract

An explicit N-fold Darboux transformation with multiparameters for a kind of coupled derivative nonlinear Schrödinger equation is constructed with the help of a gauge transformation of a spectral problem. As a reduction, a Darboux transformation of the Gerdjikov-Ivanov equation is obtained. Furthermore, the explicit soliton-like solutions of the Gerdjikov-Ivanov equation are given by applying its Darboux transformation.