arXiv subjects

Yongxing Zhu

Publications and source records attributed to Yongxing Zhu.

5 recordsLinked to original sources

arXiv2024

Quantized Vortex Dynamics of the Coupled Nonlinear Schrödinger Equation

We derive rigorously the reduced dynamical law for quantized vortex dynamics of the coupled nonlinear Schrödinger 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 Schrödinger.

math.AP↗

arXiv2023

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

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 $\varepsilon \to 0$. 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.

math.AP↗

arXiv2023

Quantized Vortex Dynamics of the Nonlinear Wave Equation on the Torus

We derive rigorously the reduced dynamical laws 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 laws are second-order nonlinear ordinary differential equations which are driven by the renormalized energy on the torus, and the initial data of the reduced dynamical laws are determined by the positions of vortices and the momentum. We will also investigate the effect of the momentum on the vortex dynamics.

math.AP↗

arXiv2023

Quantized vortex dynamics of the nonlinear Schrödinger equation on torus with non-vanishing momentum

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.

math.AP↗

arXiv2023

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

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 $\varepsilon\to 0$. 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.

math.AP↗