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.

arXiv comment54 pages, 10 figures

References in corpus (4)

• Leading Order Temporal Asymptotics of the Modified Non-Linear Schrodinger Equation: Solitonless Sector
• Long-time Asymptotics for the NLS equation via dbar methods
• On asymptotic stability of N-solitons of the defocusing nonlinear Schrodinger equation
• Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering

Cited by in corpus (4)

• Stability of multi-solitons for the derivative nonlinear Schr{ö}dinger equation
• Global Well-posedness and soliton resolution for the Derivative Nonlinear Schrödinger equation
• Instability of the solitary wave solutions for the genenalized derivative Nonlinear Schrödinger equation in the critical frequency case
• Global Well-Posesedness for the Derivative Nonlinear Schrodinger Equation