Scattering for the Quadratic Nonlinear Schrödinger System in R⁵ without Mass-Resonance Condition

Abstract

We consider the quadratic nonlinear Schrödinger system (NLS system) on R⁵. The scattering below the ground state for NLS system was obtained by the first author under the mass-resonance condition. In this paper, we prove scattering below the ground state without the mass-resonance condition under the radially symmetric assumption. Our proof is based on the concentration compactness and the rigidity by Kenig-Merle (2006). Moreover, we discuss the concentration compactness and the rigidity for non-radial solutions.