Scattering below ground states for a class of systems of nonlinear Schrodinger equations

TL;DR

This paper extends the scattering results below ground states from the single cubic nonlinear Schrödinger equation to a broad class of N-coupled systems in three dimensions, demonstrating similar scattering behavior.

Contribution

It generalizes known scattering results to N-coupled systems, expanding the understanding of nonlinear Schrödinger equations in higher dimensions.

Findings

Solutions with mass-energy below ground states scatter.

The scattering result applies to a wide class of coupled systems.

Extension of previous single-equation results to systems.

Abstract

In this paper, we consider the scattering problem for a class of $N$-coupled systems of the cubic nonlinear Schr\"odinger equations in three space dimensions. We prove the scattering of solutions that have a mass-energy quantity less than that for the ground states. This result is previously obtained by Duyckaerts-Holmer-Roudenko for the single cubic nonlinear Schr\"odinger equation in three space dimensions. It turns out that the result can be extended to a wide class of $N$-coupled systems.