Patterns in dissipative systems with weakly broken continuous symmetry.
Patterns in dissipative systems with weakly broken symmetry are studied based upon the simplest canonical equation (generalized Nikolaevskiy model). A generic cubic dispersion equation governing stability of steady spatially periodic patterns is derived and analyzed. A domain of stable states in the space of the problem parameters (stability balloon) is obtained. It is shown that the domain is characterized by unusual scaling properties, so that its different parts obey different scalings. The results obtained may be applied to describe instabilities of advancing fronts and interfaces, pattern formation in reaction-diffusion systems, nonlinear evolution of seismic waves, and other phenomena.
Tribelsky
Michael I
MI
Moscow State Institute of Radioengineering, Electronics and Automation (Technical University), Moscow, Russia. tribelsky@mirea.ru