Quantized Vortex Dynamics of the Coupled Nonlinear Schr\"odinger Equation

TL;DR

This paper rigorously derives the reduced dynamical laws governing quantized vortex motion in coupled nonlinear Schrödinger equations, showing that vortex dynamics in each component are independent as vortex core size approaches zero.

Contribution

It provides a rigorous derivation of vortex dynamics laws for coupled NLS equations, revealing independence of vortex motion between components in the small core limit.

Findings

Vortex motion laws are derived for coupled NLS equations.

Vortex dynamics in each component are independent in the small core limit.

The motion follows the vortex law for the nonlinear Schrödinger equation.

Abstract

We derive rigorously the reduced dynamical law for quantized vortex dynamics of the coupled nonlinear Schr\"odinger equation without Josephson junction (CNLS) when the core size of vortex $\varepsilon\to 0$. It is proved that when $\varepsilon\to 0$, the vortex motion of one component won't affect the vortex motion on the other component. Moreover, the motion of vortices of each component follows the vortex motion law for the nonlinear Schr\"odinger.