Scattering for quadratic-type Schr\"{o}dinger systems in dimension five without mass-resonance

TL;DR

This paper proves that non-radial solutions to a quadratic-type coupled Schrödinger system in five dimensions scatter over time, using an interaction Morawetz estimate without requiring the mass-resonance condition.

Contribution

It extends scattering results to non-radial solutions in five dimensions for quadratic Schrödinger systems without the mass-resonance assumption, employing a novel interaction Morawetz approach.

Findings

Solutions below ground state scatter in time

The method applies to non-radial solutions

No mass-resonance condition needed

Abstract

In this paper we study the scattering of non-radial solutions in the energy space to coupled system of nonlinear Schr\"{o}dinger equations with quadratic-type growth interactions in dimension five without the mass-resonance condition. Our approach is based on the recent technique introduced by Dodson and Murphy, which relies on an interaction Morawetz estimate. It is proved that any solution below the ground states scatters in time.