  Optical lattice and spin-orbit coupling are typical experimental approaches
to engineer dispersion. We reveal a self-interfering dynamics in a
noninteracting Bose-Einstein condensate with the engineered dispersion by
optical lattice or spin-orbit coupling. The self-interference results from the
co-occupation of positive and negative effect mass regimes in the engineered
dispersion. The physical origination of the self-interference is explained by
the Wigner distribution function of the self-interfering wave-packet. We
characterize detail features of the self-interference pattern.
