Double Phase Slips and Spatio-Temporal Chaos in a Model for Parametrically Excited Standing Waves

We present results of numerical simulations of coupled Ginzburg-Landau equations that describe parametrically excited waves. In one dimension we focus on a new regime in which the Eckhaus sideband instability does not lead to an overall change in the wavelength via the occurrence of a single phase slip but instead leads to ``double phase slips''. They are characterized by the phase slips occurring in sequential pairs, with the second phase slip quickly following and negating the first. The resulting dynamics range from transient excursions from a fixed point resembling those seen in excitable media, to periodic solutions of varying complexity and chaotic solutions. In larger systems we find in addition localized spatio-temporal chaos, where the solution consists of a chaotic region with quiescent regions on each side. We explain the localization using an effective phase diffusion equation which can be viewed as arising from a homogenization of the chaotic state. In two dimensions the double phase slips are replaced by fluctuating bound defect pairs.