Testing by wave packets and modified scattering in nonlinear dispersive pde's
Abstract
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely. An interesting example is that of problems with cubic nonlinearities in one space dimension. The method of testing by wave packets was introduced by the authors as a tool to efficiently capture the asymptotic equations associated to such flows, and thus establish the modified scattering mechanism in a simpler, more efficient fashion, and at lower regularity. In these expository notes we describe how this method can be applied to problems with general dispersion relations.
Cite
@article{arxiv.2204.13285,
title = {Testing by wave packets and modified scattering in nonlinear dispersive pde's},
author = {Mihaela Ifrim and Daniel Tataru},
journal= {arXiv preprint arXiv:2204.13285},
year = {2022}
}
Comments
41 pages, four figures. This is a substantial revision, with many corrections and additions and four figures added. Many thanks to the anonymous referee