Volume 57, Number 2, March-April 2023
|Page(s)||423 - 443|
|Published online||03 March 2023|
On ground state (in-)stability in multi-dimensional cubic-quintic Schrödinger equations
Univ. Rennes, CNRS IRMAR - UMR 6625, 35000 Rennes, France
2 Institut de Mathématiques de Bourgogne, Institut Universitaire de France, Université de Bourgogne-Franche-Comté, 9 avenue Alain Savary, BP 47870, 21078 Dijon Cedex, France
3 Department of Mathematics, Statistics, and Computer Science, M/C 249, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607, USA
* Corresponding author: Christian.Klein@u-bourgogne.fr
Accepted: 3 October 2022
We consider the nonlinear Schrödinger equation with a focusing cubic term and a defocusing quintic nonlinearity in dimensions two and three. The main interest of this article is the problem of orbital (in-)stability of ground state solitary waves. We recall the notions of energy minimizing versus action minimizing ground states and prove that, in general, the two must be considered as nonequivalent. We numerically investigate the orbital stability of least action ground states in the radially symmetric case, confirming existing conjectures or leading to new ones.
Mathematics Subject Classification: 35Q55 / 35C08 / 65M70
Key words: Nonlinear Schrödinger equation / solitary waves / orbital stability / time-splitting method
© The authors. Published by EDP Sciences, SMAI 2023
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