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The interacting atom-molecule BEC (AMBEC) dynamics is investigated in themean field ap- proach. The presence of atom-atom, atom-molecule andmolecule-molecule interactions, coupled with a characteristically differentinteraction representing atom-molecule interconversion, endows this system withnonlinearities, which differ significantly from the standard Gross-Pitaevskii(GP) equation. Exact localized solutions are found to belong to two distinctclasses. The first ones are analogous to the soliton solutions of the weaklycoupled GP equation, whereas the second non- equivalent class is related to thesolitons of the strongly coupled BEC. Distinct parameter domains characterizethese solitons, some of which are analogous to the complex profile Blochsolitons in magnetic systems. These localized solutions are found to representa variety of phenomena, which include co-existence of both atom-moleculecomplex and miscible-immiscible phases. Numerical sta- bility is explicitlychecked, as also the stability analysis based on the study of quantumuctuations around our solutions. We also find out the domain of modulationinstability in this system.

New cross-phase modulated localized solitons in coupled atomic-molecular BEC