Please use this identifier to cite or link to this item: https://doi.org/10.3934/dcdsb.2018096
Title: Quantized vortex dynamics and interaction patterns in superconductivity based on the reduced dynamical law
Authors: Xu, Z.
Bao, W. 
Shi, S.
Keywords: Collision cluster
Finite time collision
Interaction pattern
Non-autonomous first integral
Orbital stability
Quantized vortex
Reduced dynamical law
Superconductivity
Winding number
Issue Date: 2018
Publisher: American Institute of Mathematical Sciences
Citation: Xu, Z., Bao, W., Shi, S. (2018). Quantized vortex dynamics and interaction patterns in superconductivity based on the reduced dynamical law. Discrete and Continuous Dynamical Systems - Series B 23 (6) : 2299-2337. ScholarBank@NUS Repository. https://doi.org/10.3934/dcdsb.2018096
Rights: Attribution 4.0 International
Abstract: We study analytically and numerically stability and interaction patterns of quantized vortex lattices governed by the reduced dynamical law – a system of ordinary differential equations (ODEs) – in superconductivity. By deriving several non-autonomous first integrals of the ODEs, we obtain qualitatively dynamical properties of a cluster of quantized vortices, including global existence, finite time collision, equilibrium solution and invariant solution manifolds. For a vortex lattice with 3 vortices, we establish orbital stability when they have the same winding number and find different collision patterns when they have different winding numbers. In addition, under several special initial setups, we can obtain analytical solutions for the nonlinear ODEs. © 2018 American Institute of Mathematical Sciences. All Rights Reserved.
Source Title: Discrete and Continuous Dynamical Systems - Series B
URI: https://scholarbank.nus.edu.sg/handle/10635/212386
ISSN: 15313492
DOI: 10.3934/dcdsb.2018096
Rights: Attribution 4.0 International
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