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.