  We demonstrate theoretically and numerically that a warm fluid model of a
plasma supports space-time quasicrystalline structures. These structures are
highly nonlinear, two-phase, ion acoustic waves that are excited autoresonantly
when the plasma is driven by two small amplitude chirped-frequency
ponderomotive drives. The waves exhibit density excursions that substantially
exceed the equilibrium plasma density. Remarkably, these extremely nonlinear
waves persist even when the small amplitude drives are turned off. We derive
the weakly nonlinear analytical theory by applying Whitham's averaged
variational principle to the Lagrangian formulation of the fluid equations. The
resulting system of coupled weakly nonlinear equations is shown to be in good
agreement with fully nonlinear simulations of the warm fluid model. The
analytical conditions and thresholds required for autoresonant excitation to
occur are derived and compared to simulations. The weakly nonlinear theory
guides and informs numerical study of how the two-phase quasicrystalline
structure "melts" into a single phase traveling wave when one drive is below a
threshold. These nonlinear structures may have applications to plasma photonics
for extremely intense laser pulses, which are limited by the smallness of
density perturbations of linear waves.
