Stability of Moving Fronts in the Ginzburg-Landau Equation

Details Stability of Moving Fronts in the Ginzburg-Landau Equation Stability of Moving Fronts in the Ginzburg-Landau Equation

1993-06-21

arxiv.org/abs/chao-dyn/9306009v1

Nonlinear Sciences

Chaotic Dynamics

31 pages

Scientific paper

10.1007/BF02102640

We use Renormalization Group ideas to study stability of moving fronts in the Ginzburg-Landau equation in one spatial dimension. In particular, we prove stability of the real fronts under complex perturbations. This extends the results of Aronson and Weinberger to situations where the maximum principle is inapplicable and constitutes a step in proving the general marginal stability hypothesis for the Ginzburg-Landau equation.

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