Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line. (12th October 2017)

• Record Type: Journal Article
• Authors: Arruda, Lynnyngs Kelly; Lenells, Jonatan
• Is Part Of: Nonlinearity. Volume 30:Number 11(2017:Nov.)
• Page Start: 4141
• Page End: 4172
• Publication Date: 2017-10-12
• Subjects: nonlinear steepest descent -- initial-boundary value problem -- Riemann–Hilbert problem -- asymptotics; 35Q55 -- 35Q15 -- 41A60; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa84c6
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We derive asymptotic formulas for the solution of the derivative nonlinear Schrödinger equation on the half-line under the assumption that the initial and boundary values lie in the Schwartz class. The formulas clearly show the effect of the boundary on the solution. The approach is based on a nonlinear steepest descent analysis of an associated Riemann–Hilbert problem.