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arXiv · 2511.00474

Sharp Stability of Solitons for the Cubic-Quintic NLS on R^2

Yi Jiang·Chenglin Wang·Yibin Xiao·Jian Zhang·Shihui Zhu
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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.

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Yi Jiang, Chenglin Wang, Yibin Xiao, Jian Zhang, Shihui Zhu. 2025-11-01. Sharp Stability of Solitons for the Cubic-Quintic NLS on R^2. https://arxiv.org/abs/2511.00474

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