  We present a theoretical analysis of three-dimensional (3D) matter-wave
solitons and their stability properties in coupled atomic and molecular
Bose-Einstein condensates (BEC). The soliton solutions to the mean-field
equations are obtained in an approximate analytical form by means of a
variational approach. We investigate soliton stability within the parameter
space described by the atom-molecule conversion coupling, atom-atom s-wave
scattering, and the bare formation energy of the molecular species. In terms of
ordinary optics, this is analogous to the process of sub/second-harmonic
generation in a quadratic non-linear medium modified by a cubic nonlinearity,
together with a phase mismatch term between the fields. While the possibility
of formation of multidimensional spatio-temporal solitons in pure quadratic
media has been theoretically demonstrated previously, here we extend this
prediction to matter-wave interactions in BEC systems where higher-order
non-linear processes due to interparticle collisions are unavoidable and may
not be neglected. The stability of the solitons predicted for repulsive
atom-atom interactions is investigated by direct numerical simulations of the
equations of motion in a full 3D lattice. Our analysis also leads to a possible
technique for demonstrating the ground state of the Schroedinger-Newton and
related equations that describe Bose-Einstein condensates with non-local
inter-particle forces.
