The interacting atom-molecule BEC (AMBEC) dynamics is investigated in the mean field ap- proach. The presence of atom-atom, atom-molecule and molecule-molecule interactions, coupled with a characteristically different interaction representing atom-mo
lecule interconversion, endows this system with nonlinearities, which differ significantly from the standard Gross-Pitaevskii (GP) equation. Exact localized solutions are found to belong to two distinct classes. The first ones are analogous to the soliton solutions of the weakly coupled GP equation, whereas the second non- equivalent class is related to the solitons of the strongly coupled BEC. Distinct parameter domains characterize these solitons, some of which are analogous to the complex profile Bloch solitons in magnetic systems. These localized solutions are found to represent a variety of phenomena, which include co-existence of both atom-molecule complex and miscible-immiscible phases. Numerical sta- bility is explicitly checked, as also the stability analysis based on the study of quantum uctuations around our solutions. We also find out the domain of modulation instability in this system.
