Abstract
We consider the problem of formation of small amplitude spatially localized oscillatory structures for atomic Bose-Einstein condensate (BEC) confined in two and three dimensional optical lattices (OL's), respectively. By using kp-method we have demonstrated mapping of the initial Gross-Pitaevskii equation on nonlinear Klein-Gordon equations. Formation of breather-like oscillating localized states-atomic oscillons-have been predicted in this case.