  We investigate the possibility of creating X-waves, or localized wave
packets, in resonantly excited exciton-polariton superfluids. We demonstrate
the existence of X-wave traveling solutions in the coupled exciton-photon
system past the inflection point, where the effective mass of lower polaritons
is negative in the direction perpendicular to the wavevector of the pumping
beam. Contrary to the case of bright solitons, X-waves do not require
nonlinearity for sustaining their shape. Nevertheless, we show that
nonlinearity is important for their dynamics, as it allows for their
spontaneous formation from an initial Gaussian wave packet. Unique properties
of exciton-polaritons may lead to applications of their X-waves in
long-distance signal propagation inside novel integrated optoelectronic
circuits based on excitons.
