Short-wavelength instability in presence of a zero mode: Anomalous growth law

A nonlinear model that combines onset of nonoscillatory short-wavelength instability and a long-wave zero mode is investigated numerically. Due to the coupling to the zero mode, the system's dynamics drastically differs from those in traditional short-wavelength models. In agreement with independent recently published results, we conclude that, immediately beyond the instability threshold, the system demonstrates a chaotic behavior, which makes it cognate to the long-wave systems. An essentially novel result is that a mean amplitude of the dynamical patterns grows linearly with the overcriticality. The corresponding scaling power 1 is just between the values 1/2 and 3/2, characteristic, respectively, for the traditional short- and long-wave models. (C) 1997 Elsevier Science B.V.