Decay and Scattering of Solutions to Nonlinear Schrödinger Equations with Regular Potentials for Nonlinearities of Sharp Growth (Journal of Mathematical Study, 2017)
In this paper, we prove the decay and scattering in the energy space for nonlinearSchrödinger equations with regular potentials in $\mathbb{R}^d$ namely, $i∂_tu+Δu-V(x)u+λ|u|^{p-1}u=0$. We will prove decay estimate and scattering of the solution in the smalldata case when $1+\frac{2}{d}
Keywords: Nonlinear Schrödinger equations; potential; decay; scattering.