Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2006-09-29
Phys. Rev. E 75, 036604 (2007)
Nonlinear Sciences
Pattern Formation and Solitons
7 pages, 5 eps figures
Scientific paper
10.1103/PhysRevE.75.036604
We show the existence of steadily moving solitary pulses (SPs) in the complex Ginzburg-Landau (CGL) equation, which includes the cubic-quintic (CQ) nonlinearity and a conservative linear driving term, whose amplitude is a standing wave with wavenumber $k$ and frequency $\omega $, the motion of the SPs being possible at velocities $\pm \omega /k$, which provide locking to the drive. A realization of the model may be provided by 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.
Baizakov Bakhtiyor B.
Filatrella Giovanni
Malomed Boris A.
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