We propose a new Landau-Ginzburg theory for arbitrarily shaped vortex strings in superfluid He. The theory contains a topological term and directly describes vortex dynamics. We introduce gauge fields in order to remove singularities from the Landau-Ginzburg order parameter of the superfluid, so that two kinds of gauge symmetries appear, making the continuity equation and conservation of the to...

{ In direct simulations of the anisotropic complex Ginzburg-Landau equation periodic defect chain structures are found. They develop spontaneously in a small parameter region, but once initialized their range of stable existence is rather large. We discuss diierent types found in diierent parameter regions.

It is shown that the complex Ginzburg-Landau (CGL) equation on the real line admits nontrivial 2-periodic vortex solutions that have 2n simple zeros (\vortices") per period. The vortex solutions bifurcate from the trivial solution and inherit their zeros from the solution of the linearized equation. This result rules out the possibility that the vortices are determining nodes for vortex solutio...

We have found a dissipative soliton resonance which applies to nonlinear dynamical systems governed by the complex cubic-quintic Ginzburg-Landau equation. Specifically, for particular values of the equation parameters, the soliton energy increases indefinitely. These equation parameters can easily be found using approximate methods, and the results agree very well with numerical ones. The pheno...