Dynamics of overlapping vortices in complex scalar fields
Abstract
Description
We investigate dynamics of overlapping vortices in the nonlinear Schrödinger equation, the nonlinear heat equation and in the equation with an intermediate Schrödinger-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.
detailed analysis of the continuation in the complex time plane; latest revision: the paper is made more readable. 9 pages in Latex
detailed analysis of the continuation in the complex time plane; latest revision: the paper is made more readable. 9 pages in Latex