2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147499We 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 LatexCondensed MatterHigh Energy Physics - PhenomenologyHigh Energy Physics - Theorytext