A new proof of scattering below the ground state for the non-radial focusing NLS

Abstract

We revisit the scattering result of Duyckaerts, Holmer, and Roudenko for the non-radial ${\dot{H}}^{1/2}$-critical focusing NLS. By proving an interaction Morawetz inequality, we give a simple proof of scattering below the ground state in dimensions $d\ge 3$ that avoids the use of concentration compactness.

14 pages