  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-molecule 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.
