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.
|Translated title of the contribution||Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data|
|Number of pages||49|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|State||Published - Jan 2018|
Bibliographical noteFunding Information:
P. Perry supported in part by a Simons Research and Travel Grant 359431 . C. Sulem supported in part by NSERC Grant 46179-13 .
© 2017 Elsevier Masson SAS
- Inverse scattering method
- Nonlinear steepest descent method
- Riemann–Hilbert problem
ASJC Scopus subject areas
- Mathematical Physics
- Applied Mathematics