Phase Ordering Dynamics in the Complex Ginzburg-Landau Equation

Abstract

There has been intense interest in problems of pattern formation in biological systems and chemical reactions [327–331]. In general, many physical systems exhibit fascinating spatio-temporal dynamics, resulting from the emergence and interaction of spatially-extended structures, e.g., vortices, spirals, etc. In this context [327–333], much attention has focused on the complex Ginzburg-Landau (CGL) equation, which has the general form:

$$\frac{\partial }{{\partial t}}\psi (r,t)\; = \;\psi + (1 + ia){\nabla ^2}\psi - (1 + i\beta ){\text{|}}\psi {{\text{|}}^{\text{2}}}\psi $$

(6.1)

.