We investigate the propagation of localized three-dimensional spatiotemporal Airy self-accelerating parabolic-cylinder light bullets in a linear medium. In particular, we consider the effects resulting from utilizing initial finite-energy Airy wave packets to accelerate these localized beams in the absence of any external potential. A general localized light bullet solution with the joint Airy pulse characteristics and parabolic-cylinder spatial characteristics is obtained in the Cartesian coordinates, using parabolic-cylinder and Airy functions. Our results show that the localized wave packets can retain their intensity features and still be accelerated over several Rayleigh lengths. 2013 American Physical Society.
