Asymptotic behavior of nonlinear Schroedinger Systems with Linear Coupling

TL;DR

This paper analyzes the long-term behavior of a coupled nonlinear Schrödinger system with linear coupling, proving convergence and global existence results for large Rabi frequencies, which model external driven fields.

Contribution

It provides the first asymptotic analysis of coupled nonlinear Schrödinger systems with linear coupling, establishing convergence and global existence criteria.

Findings

Convergence in Strichartz space for large Rabi frequency

Global existence of the limiting system

Asymptotic behavior characterized for large coupling

Abstract

A system of two coupled nonlinear Schroedinger equations is treated. In addition, a linear coupling which models an external driven field described by the Rabi frequency is considered. Asymptotics for large Rabi frequency are carried out. Convergence in the appropriate Strichartz space is proven. As a consequence, the global existence of the limiting system gives a criterion for the long time behavior of the original system.