  We demonstrate the occurrence of oscillatory reactions in the ultra-cold
chemistry of atom-molecular Bose-Einstein condensate. Nonlinear oscillations in
the mean-field dynamics occur for a specific range of elliptic modulus, giving
rise to both in- and out-phase modulations in the atom-molecule population
density. The reaction front velocity is found to be controlled by
photoassociation, which also regulates the condensate density. Two distinct
pair of in-phase bright localized gap solitons are found as exact solutions,
existence of one of which necessarily requires a background. Cnoidal atomic
density-waves in a plane wave molecular background are observed in both
attractive and repulsive domains. Role of intra- and inter-species interactions
on both existence and stability is explicated in the presence of
photoassociation.
