Sharp Stability of Solitons for the Cubic-Quintic NLS on R^2
Analysis of PDEs
2025-11-04 v1
Abstract
This paper concerns with the cubic-quintic nonlinear Schr\"{o}dinger equation on R^2. A family of new variational problems related to the solitons are introduced and solved. Some key monotonicity and uniqueness results are obtained. Then the orbital stability of solitons at every frequency are proved in terms of the Cazenave and Lions' argument. And classification of normalized ground states is first presented. Our results settle the questions raised by Lewin and Rota Nodari as well as Carles and Sparber.
Keywords
Cite
@article{arxiv.2511.00474,
title = {Sharp Stability of Solitons for the Cubic-Quintic NLS on R^2},
author = {Yi Jiang and Chenglin Wang and Yibin Xiao and Jian Zhang and Shihui Zhu},
journal= {arXiv preprint arXiv:2511.00474},
year = {2025}
}