Quantized vortex dynamics of the nonlinear Schrödinger equation on torus with non-vanishing momentum
arXiv:2304.02987 · doi:10.1016/j.physd.2023.133812
Abstract
We derive rigorously the reduced dynamical laws for quantized vortex dynamics of the nonlinear Schrödinger equation on the torus with non-vanishing momentum when the vortex core size ε \to 0. The reduced dynamical laws are governed by a Hamiltonian flow driven by a renormalized energy. A key ingredient is to construct a new canonical harmonic map to include the effect from the non-vanishing momentum into the dynamics. Finally, some properties of the reduced dynamical law are discussed.
20 pages