Localized structures in nonequilibrium systems
We study numerically a prototype equation which arises generically as an envelope equation for a weakly inverted bifurcation associated to traveling waves: The complex quintic Ginzburg-Landau equation. We show six different stable localized structures including stationary pulses, moving pulses, stationary holes and moving holes, starting from localized initial conditions with periodic and Neumann boundary conditions.
ginzburg-landau equation oscillatory instability localized solutions