On ground state (in-)stability in multi-dimensional cubic-quintic 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 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.

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

Rémi Carles, Christian Klein, Christof Sparber. On ground state (in-)stability in multi-dimensional cubic-quintic Schrödinger equations. ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57 (2), pp.423-443. ⟨10.1051/m2an/2022085⟩. ⟨hal-03085923v2⟩