Long-Time Behavior of Solutions to the Derivative Nonlinear Schrödinger Equation for Soliton-Free Initial Data

Abstract

The large-time behavior of solutions to the derivative nonlinear Schrödinger 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.

54 pages, 10 figures

References in corpus (1)

• Long-time Asymptotics for the NLS equation via dbar methods

Cited by in corpus (3)

• Stability of multi-solitons for the derivative nonlinear Schr{ö}dinger equation
• Global Well-posedness and soliton resolution for the Derivative Nonlinear Schrödinger equation
• Global Well-Posesedness for the Derivative Nonlinear Schrodinger Equation