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

We consider the nonlinear Schrödinger equation with a focusing cubic term and defocusing quintic nonlinearity in dimensions two three. The main interest of this article is problem orbital (in-)stability ground state solitary waves. recall notions energy minimizing versus action states prove that, general, must be considered as nonequivalent. numerically investigate stability least radially symmetric case, confirming existing conjectures or leading to new ones.