Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation

Abstract

In this paper, we consider a class of the defocusing inhomogeneous nonlinear Schrödinger equation i∂tu+Δu-|x|-b|u|αu=0,u(0)=u0∈H1,with b, α> 0. We first study the decaying property of global solutions for the equation when 0 < α< α ⋆ where α⋆=4-2bd-2 for d≥ 3. The proof makes use of an argument of Visciglia (Math Res Lett 16(5):919–926, 2009). We next use this decay to show the energy scattering for the equation in the case α ⋆ < α< α ⋆ , where α⋆=4-2bd.