  Recent results from linear perturbation theory suggest that first-order
cosmological quark-hadron phase transitions occurring as deflagrations may be
``borderline'' unstable, and those occurring as detonations may give rise to
growing modes behind the interface boundary. However, since nonlinear effects
can play important roles in the development of perturbations, unstable behavior
cannot be asserted entirely by linear analysis, and the uncertainty of these
recent studies is compounded further by nonlinearities in the hydrodynamics and
self-interaction fields. In this paper we investigate the growth of
perturbations and the stability of quark-hadron phase transitions in the early
Universe by solving numerically the fully nonlinear relativistic hydrodynamics
equations coupled to a scalar field with a quartic self-interaction potential
regulating the transitions. We consider single, perturbed, phase transitions
propagating either by detonation or deflagration, as well as multiple phase and
shock front interactions in 1+2 dimensional spacetimes.
