Counterpropagating periodic pulses in coupled Ginzburg-Landau equations

Abstract

A recently observed stable regime in the form of periodically colliding counterpropagating wave packets (pulses) in an annular convection channel at very small positive overcriticalities is described analytically in terms of coupled Ginzburg-Landau equations. First, the existence of this regime is demonstrated in the framework of the simplest system including only the group-velocity difference, weak gain, and nonlinear dissipative coupling between two modes. In this approximation, the shape of the counterpropagating waves remains indefinite. It is demonstrated that additional dispersive terms, regarded as a small perturbation, provide shaping of the wave packets and also give rise to the deviation of the phase velocity from that for purely linear waves.