Long-time asymptotic for the derivative nonlinear Schrödinger equation with decaying initial value

2012/09/30 by Jian Xu, Engui Fan · 2 citations
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1007/s11040-013-9132-3

41 pages

arxiv created 2012/11/26 · arxiv updated 2015/06/11

Abstract

We present a new Riemann-Hilbert problem formalism for the initial value problem for the derivative nonlinear Schrödinger (DNLS) equation on the line. We show that the solution of this initial value problem can be obtained from the solution of some associated Riemann-Hilbert problem. This new Riemann-Hilbert problem for the DNLS equation will lead us to use nonlinear steepest-descent/stationary phase method or Deift-Zhou method to derive the long-time asymptotic for the DNLS equation on the line.

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• Numerical inverse scattering transform for the coupled modified Korteweg-de Vries equation

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