English

Quantized vortex dynamics of the complex Ginzburg-Landau equation on torus

Analysis of PDEs 2024-06-25 v1 Dynamical Systems

Abstract

We derive rigorously the reduced dynamical laws for quantized vortex dynamics of the complex Ginzburg-Landau equation on torus when the core size of vortex ε0\varepsilon\to 0. The reduced dynamical laws of the complex Ginzburg-Landau equation are governed by a mixed flow of gradient flow and Hamiltonian flow which are both driven by a renormalized energy on torus. Finally, some first integrals and analytic solutions of the reduced dynamical laws are discussed.

Keywords

Cite

@article{arxiv.2304.08301,
  title  = {Quantized vortex dynamics of the complex Ginzburg-Landau equation on torus},
  author = {Yongxing Zhu},
  journal= {arXiv preprint arXiv:2304.08301},
  year   = {2024}
}