Existence and stability of solitons for the nonlinear Schr\"odinger equation on hyperbolic space
Analysis of PDEs
2015-05-13 v5
Abstract
We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of Euclidean space.
Keywords
Cite
@article{arxiv.0905.1848,
title = {Existence and stability of solitons for the nonlinear Schr\"odinger equation on hyperbolic space},
author = {Hans Christianson and Jeremy Marzuola},
journal= {arXiv preprint arXiv:0905.1848},
year = {2015}
}
Comments
New: As noted in Banica-Duyckaerts (arXiv:1411.0846), Section 5 should read that for sufficiently large mass, sub-critical problems can be solved via energy minimization for all d \geq 2 and as a result Cazenave-Lions results can be applied in Section 6 with the same restriction. These requirements were addressed by the subsequent work with Metcalfe and Taylor in arXiv:1203.3612