Scattering solutions to nonlinear Schrödinger equation with a long range potential

Abstract

In this paper, we consider a nonlinear Schrödinger equation with a repulsive inverse-power potential. It is known that the corresponding stationary problem has a "radial" ground state. Here, the "radial" ground state is a least energy solution among radial solutions to the stationary problem. We prove that if radial initial data below the "radial" ground state has positive virial functional, then the corresponding solution to the nonlinear Schrödinger equation scatters. In particular, we can treat not only short range potentials but also long range potentials.

30 pages