Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line

2017/02/07 by Lynnyngs Kelly Arruda, Jonatan Lenells, Arruda, L. K. +1 · 2 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1702.02084

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.

Citations

• On the modulational instability of hydromagnetic waves parallel to the magnetic field

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• The initial-boundary value problems for the coupled derivative nonlinear Schrödinger equations on the half-line
• A Riemann-Hilbert Approach to the Kundu-Eckhaus Equation on the half-Line

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