Quantized Vortex Dynamics of the Nonlinear Schrödinger Equation with Wave Operator on the Torus

Abstract

We derive rigorously the reduced dynamical law for quantized vortex dynamics of the nonlinear Schrödinger equation with wave operator on the torus when the core size of vortex $\epsilon \to 0$. It is proved that the reduced dynamical law of the nonlinear Schrödinger equation with wave operator is a mixed state of the vortex motion laws for the nonlinear wave equation and the nonlinear Schrödinger equation. We will also investigate the convergence of the reduced dynamical law of the nonlinear Schrödinger equation with wave operator to the vortex motion law of the nonlinear Schrödinger equation via numerical simulation.

15 pages