  We apply the averaging method to analyze spatio-temportal structures in
nonlinear Schr\"odinger equations and thereby study the dynamics of
quasi-one-dimensional collisionally inhomogeneous Bose-Einstein condensates
with the scattering length varying periodically in spatial and crossing zero.
Infinitely many (positive measure set) modulated amplitude waves (periodic and
quasi-periodic), which are instable, can be proved to exist by adjusting the
intergration constant c on some open interval. Finally, some numerical
simulations support our results.
