  We study dynamics of a two-color photoassociation of atoms into diatomic
molecules via nonlinear Stimulated Raman adiabatic passage (STIRAP) process.
This system has a famous counterpart in (linear) quantum mechanics, and been
discussed recently in the context of generalizing quantum adiabatic theorem to
nonlinear systems. Here we use another approach to study adiabaticity and
stability in the system: we apply methods of classical Hamiltonian dynamics. We
found nonlinear dynamical instabilities, cases of complete integrability, and
improved conditions of adiabaticity.
