Abstract
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 pairs of in-phase bright localized gap solitons are found as exact solutions, the existence of one of which necessarily requires a background. Cnoidal atomic density waves along with a plane-wave molecular motion are observed in both attractive and repulsive domains. The role of intra- and inter-species interactions on both existence and stability is explicated in the presence of photoassociation.
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