Double Scattering Channels for $1D$ NLS in the Energy Space and its Generalization to Higher Dimensions
Analysis of PDEs
2017-09-18 v2
Abstract
We consider a class of NLS perturbed with a steplike potential. We prove that the nonlinear solutions satisfy the double scattering channels in the energy space. The proof is based on concentration-compactness/rigidity method. We prove moreover that in dimension higher than one, classical scattering holds if the potential is periodic in all but one dimension and is steplike and repulsive in the remaining one.
Keywords
Cite
@article{arxiv.1610.05496,
title = {Double Scattering Channels for $1D$ NLS in the Energy Space and its Generalization to Higher Dimensions},
author = {Luigi Forcella and Nicola Visciglia},
journal= {arXiv preprint arXiv:1610.05496},
year = {2017}
}
Comments
Extended (revised) version in $\mathbb R^d$ of the previous paper. Accepted: JDE