Long-time asymptotic for the derivative nonlinear Schr\"odinger equation with decaying initial value
Exactly Solvable and Integrable Systems
2015-06-11 v2
Abstract
We present a new Riemann-Hilbert problem formalism for the initial value problem for the derivative nonlinear Schr\"odinger (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.
Keywords
Cite
@article{arxiv.1209.4245,
title = {Long-time asymptotic for the derivative nonlinear Schr\"odinger equation with decaying initial value},
author = {Jian Xu and Engui Fan},
journal= {arXiv preprint arXiv:1209.4245},
year = {2015}
}
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41 pages