Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space
Analysis of PDEs
2007-05-23 v2
Abstract
The authors compute the long-time asymptotics for solutions of the NLS equation just under the assumption that the initial data lies in a weighted Sobolev space. In earlier work (see e.g. [DZ1],[DIZ]) high orders of decay and smoothness are required for the initial data. The method here is a further development of the steepest descent method of [DZ1], and replaces certain absolute type estimates in [DZ1] with cancellation from oscillations.
Keywords
Cite
@article{arxiv.math/0206222,
title = {Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space},
author = {P. Deift and X. Zhou},
journal= {arXiv preprint arXiv:math/0206222},
year = {2007}
}