Stability of ground states of NLS with fourth order dispersion

Abstract

In this paper, we investigate the existence, uniqueness and stability of the ground states of nonlinear Schrödinger type equations with a small fourth order dispersion. Such equations appear in the higher order approximation of the propagation of laser beam in Kerr medium. We show that for the critical case, the ground state, which is unstable in the absence of the fourth order dispersion, becomes stable with small fourth order term.