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

2016/08/27 by Liu, Jiaqi, Perry, Peter, Sulem, Catherine · 1 citation
#35Q15 #35Q55 #37K10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.07659

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.

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