Moving and colliding pulses in the subcritical Ginzburg-Landau model with a standing-wave drive

We show the existence of steadily moving solitary pulses SPs in the complex Ginzburg-Landau equation, which includes the cubic-quintic nonlinearity and a conservative linear driving term, whose amplitude is a standing wave with wave number k and frequency , the motion of the SPs being possible at resonant velocities ±/k, which provide for locking to the drive. The model may be realized in terms of traveling-wave convection in a narrow channel with a standing wave excited in its bottom or on the surface. An analytical approximation is developed, based on an effective equation of motion for the SP coordinate. Direct simulations demonstrate that the effective equation accurately predicts characteristics of the driven motion of pulses, such as a threshold value of the drive’s amplitude. Collisions between two solitons traveling in opposite directions are studied by means of direct simulations, which reveal that they restore their original shapes and velocity after the collision.