Asymptotic behavior of solutions to the cubic coupled Schr\"odinger systems in one space dimension

TL;DR

This paper investigates the long-term behavior of solutions to a coupled cubic nonlinear Schrödinger system in one dimension, revealing asymptotic decay and nonlinear dynamics relevant to optical waveguides.

Contribution

It establishes the asymptotic behavior and decay estimates for solutions of the coupled Schrödinger system, extending understanding of nonlinear wave interactions in optical contexts.

Findings

Solutions exhibit specific decay rates over time.

Asymptotic nonlinear behavior is characterized.

Results are applicable to optical waveguide coupling.

Abstract

In this paper, we study a coupled nonlinear Schr{\"o}dinger system with small initial data in the one dimension Euclidean space. Such a system appears in the context of the coupling between two different optical waveguides. We establish an asymptotic nonlinear behavior and a decay estimate for solutions of this system. The proof uses a recent work of Kato and Pusateri.