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On soliton (in-)stability in multi-dimensional cubic-quintic nonlinear Schrödinger equations

Abstract : We consider the nonlinear Schrödinger equation with a focusing cubic term and a defocusing quintic nonlinearity in dimensions two and three. The core of this article is the notion of stability of solitary waves. We recall the two standard notions of orbital stability in the context of nonlinear Schrödinger equations, and show that they must be considered as independent from each other. We investigate numerically the notion of orbital stability of ground states in the radially symmetric case, confirming existing conjectures or leading to new ones.
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Contributor : Rémi Carles <>
Submitted on : Tuesday, December 22, 2020 - 10:14:23 AM
Last modification on : Thursday, January 28, 2021 - 10:28:03 AM


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  • HAL Id : hal-03085923, version 1


Rémi Carles, Christian Klein, Christof Sparber. On soliton (in-)stability in multi-dimensional cubic-quintic nonlinear Schrödinger equations. 2020. ⟨hal-03085923⟩



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