  The free particle Schrodinger equation admits a non-trivial self-accelerating
Airy wave packet solution. Recently, the Airy beams that freely accelerate in
space was experimentally realized in photonics community. Here we present
self-accelerating waves for the Bose-Einstein condensate in a time dependent
harmonic oscillator potential. We show that parity and time reversal symmetries
for self accelerating waves are spontaneously broken.
