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

Rémi Carles (1) , Christian Klein (2) , Christof Sparber (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 UIC - Department of Mathematics, Statistics and Computer Science [Chicago]

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.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Physique mathématique [math-ph]

Rémi Carles, Christian Klein, Christof Sparber. On soliton (in-)stability in multi-dimensional cubic-quintic nonlinear Schrödinger equations. 2020. ⟨hal-03085923v1⟩