Long-Time Asymptotics for the Combined Nonlinear Schrödinger and Gerdjikov-Ivanov Equation

Abstract

In this paper, the combined nonlinear Schrödinger and Gerdjikov-Ivanov (NLS-GI) equation with the Schwartz initial data is investigated. It is shown that the solution of NLS-GI equation can be expressed in terms of the solution associated with a Riemann-Hilbert (RH) problem. The long-time asymptotics is further obtained via the Deift-Zhou nonlinear steepest descent method.