Ground states for Schrödinger-type equations with nonlocal nonlinearity

The problem of the existence of stable solitary wave solutions for nonlinear Schrödinger-type equations with a generalized cubic nonlinearity is considered. These types of equations have recently arisen in the context of optical communications as averaging approximations to nonlinear dispersive equations with widely separated time scales. In this paper, it is shown that under general conditions on the kernel of the nonlocal term, stable standing wave solutions exist for these equations.