Localized structures in nonequilibrium systems

Abstract

We study numerically a prototype equation which arises generically as an envelope equa- tion for a weakly inverted bifurcation associated to traveling waves: The complex quintic Ginzburg{Landau equation. We show six di erent stable localized structures including stationary pulses, moving pulses, stationary holes and moving holes, starting from lo- calized initial conditions with periodic and Neumann boundary conditions.