Scattering of radial solutions for quadratic-type Schr\"{o}dinger systems in dimension five

TL;DR

This paper investigates the scattering behavior of radial solutions to a multi-component quadratic Schrödinger system in five dimensions, employing advanced analytical techniques to establish new scattering results.

Contribution

It introduces a novel application of Dodson and Murphy's method to multi-component quadratic Schrödinger systems in five dimensions.

Findings

Proves scattering for radial solutions in the specified system.

Utilizes radial Sobolev embedding and Morawetz estimates effectively.

Extends existing techniques to multi-component systems.

Abstract

In this paper we study the scattering of radial solutions to a $l$-component system of nonlinear Schr\"{o}dinger equations with quadratic-type growth interactions in dimension five. Our approach is based on the recent technique introduced by Dodson and Murphy, which relies on the radial Sobolev embedding and a Morawetz estimate.