| Contents |
| In this talk we study, the stability of radially
symmetric blowup solutions of the Ginzburg-Landau equation with respect to radially symmetric and
non-radially symmetric perturbations.
Upon writing the Ginzburg-Landau equation as a small perturbation
of the nonlinear Schr\"odinger equation, the existence of
multi-bump blowup solutions, especially of
ring-like solutions, has already been established.
So far, the stability of these blowup solutions had only been
examined numerically. We use Evans function techniques
developed for perturbations of Hamiltonian systems to study
the stability of the ring-type solutions depending on the
parameters in the system.
The application of these methods is not straightforward and they have to be
modified to suit our system. |
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