# Large time asymptotics for a cubic nonlinear Schr\"odinger system in one space dimension

## TL;DR

This paper studies the long-term behavior of a two-component cubic nonlinear Schrödinger system in one dimension, revealing that solutions resemble free solutions over time with specific profile restrictions due to long-range interactions.

## Contribution

It demonstrates the asymptotic free behavior of solutions and uncovers the influence of long-range nonlinear interactions on profile restrictions.

## Key findings

- Solutions behave like free solutions at large times
- Profiles of components are strongly restricted by nonlinear interactions
- Long-range effects significantly influence asymptotic behavior

## Abstract

We consider a two-component system of cubic nonlinear Schr\"odinger equations in one space dimension. We show that each component of the solutions to this system behaves like a free solution in the large time, but there is a strong restriction between the profiles of them. This turns out to be a consequence of non-trivial long-range nonlinear interactions.