Dynamics of overlapping vortices in complex scalar fields
Abstract
We investigate dynamics of overlapping vortices in the nonlinear Schr\"{o}dinger equation, the nonlinear heat equation and in the equation with an intermediate Schr\"{o}dinger-diffusion dynamics. Because of formal similarity on a perturbative level we discuss also the nonlinear wave equation (Goldstone model). Special solutions are found like vortex helices, double-helices and braids, breather states and vortex mouths. A pair of vortices in the Goldstone model scatters by the right angle in the head-on collision. It is found that in a dissipative system there is a characteristic lenght scale above which vortices can be entangled but below which the entanglement is unstable.
Cite
@article{arxiv.cond-mat/9503068,
title = {Dynamics of overlapping vortices in complex scalar fields},
author = {Jacek Dziarmaga},
journal= {arXiv preprint arXiv:cond-mat/9503068},
year = {2008}
}
Comments
detailed analysis of the continuation in the complex time plane; latest revision: the paper is made more readable. 9 pages in Latex