Mathematical Foundations of Ginzburg Landau Theory

Ian Melbourne

University of Surrey, UK

We consider mathematical issues concerning Ginzburg-Landau theory, including the validity, universality, and structure of reduced equations near criticality in spatially extended systems. The extraction of Ginzburg-Landau equations (variously known as amplitude, modulation and envelope equations) is part of this theory.

We pay particular attention to the (noncompact) Euclidean symmetries present in such systems, stressing the analogy with Landau theory (where the symmetry group is finite) and equivariant bifurcation theory (where the symmetry group is compact).