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

22 pagesWe consider the nonlinear Schrödinger equation with a focusing cubicterm and a defocusing quintic nonlinearity in dimensions two andthree. The main interest of this article is the problem of orbital (in-)stability of ground state solitarywaves. 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