Long-Time Behavior of Solutions to the Derivative Nonlinear Schr\"{o}dinger Equation for Soliton-Free Initial Data

Abstract

The large-time behavior of solutions to the derivative nonlinear Schr\"{o}dinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin.