Long-Time Behavior of Solutions to the Derivative Nonlinear Schr\"{o}dinger Equation for Soliton-Free Initial Data
Analysis of PDEs
2016-08-30 v1
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.
Keywords
Cite
@article{arxiv.1608.07659,
title = {Long-Time Behavior of Solutions to the Derivative Nonlinear Schr\"{o}dinger Equation for Soliton-Free Initial Data},
author = {Jiaqi Liu and Peter Perry and Catherine Sulem},
journal= {arXiv preprint arXiv:1608.07659},
year = {2016}
}
Comments
54 pages, 10 figures