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