$$H^1$$ Scattering for Mass-Subcritical NLS with Short-Range Nonlinearity and Initial Data in $$\Sigma $$

Abstract

AbstractWe consider short-range mass-subcritical nonlinear Schrödinger equations, and we show that the corresponding solutions with initial data in $$\Sigma $$ Σ scatter in $$H^1$$ H 1 . Hence we up-grade the classical scattering result proved by Yajima and Tsutsumi from $$L^2$$ L 2 to $$H^1$$ H 1 . We also provide some partial results concerning the scattering of the first order moments, as well as a short proof via lens transform of a classical result due to Tsutsumi and Cazenave–Weissler on the scattering in $$\Sigma $$ Σ .