Motion of pulses and vortices in the cubic-quintic complex Ginzburg-Landau equation without viscosity

Motions of pulses and vortices are numerically studied with the cubic-quintic complex Ginzburg-Landau equation without viscous terms. There exist moving pulses and vortices with any velocities, because the equation is invariant for the Galilei transformation. We study mutual collisions of counter-propagating pulses and vortices, and motions of pulses and vortices in external potentials. Moving pulses and vortices pass through a potential wall like a tunnel effect. If some viscous terms are included, the model equation is equivalent to the quintic complex Swift-Hohenberg equation. We find a supercritical bifurcation from a stationary pulse to a moving pulse.