Waves and solitary pulses in a weakly inhomogeneous Ginzburg-Landau system

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Abstract
Dynamics of continuous waves (cw’s) and solitary pulses (SP’s) are considered in the cubic complex Ginzburg-Landau equation with x-dependent coefficients in front of the linear terms, which is a natural model of the traveling-wave convection in a narrow slightly inhomogeneous channel. For the cw, it is demonstrated that even a weak inhomogeneity can easily render all the waves unstable, which may be one of the factors stipulating the so-called dispersive chaos experimentally observed in the convection. Evolution of a SP in the presence of a smooth inhomogeneity is considered by means of the perturbation theory, and it is demonstrated that, in accordance with experimental observations, the spot that is most apt to trap the pulse is the spot with a maximum slope of the inhomogeneity.