Work

Quantized vortex dynamics of the nonlinear wave equation on the torus

Year: 2023

Type: article

Abstract: We rigorously derive the reduced dynamical law for quantized vortex dynamics of the nonlinear wave equation on the torus when the core size of vortex $ \varepsilon\to 0 $. It is proved that the reduced dynamical law is a system consisting of second-order nonlinear ordinary differential equations driven by the renormalized energy on the torus, and the initial data of the reduced dynamical law is determined by the positions of vortices and the limit momentum of the solution of the nonlinear wave equation. We will also investigate the effect of the limit momentum on the vortex dynamics via numerical simulation.

Source: Discrete and Continuous Dynamical Systems - B

DOI: 10.3934/dcdsb.2023188

Author: Yongxing Zhu

Institution: Tsinghua University

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National University of Singapore, National Natural Science Foundation of China, Tsinghua University, China Scholarship Council

Awards: G1678429644, G3193396747, 凸几何中蒙日-安培型方程的研究