  We discuss the strong interaction regime of the nonlinear Landau-Zener
problem coming up at coherent photo- and magneto-association of ultracold
atoms. We apply a variational approach to an exact third-order nonlinear
differential equation for the molecular state probability and construct an
accurate approximation describing the whole time dynamics of the coupled
atom-molecular system. The resultant solution improves the accuracy of the
previous approximation by A. Ishkhanyan et al. [J. Phys. A 39, 14887 (2006)].
The obtained results reveal a remarkable observation that in the strong
coupling limit the resonance crossing is mostly governed by the nonlinearity
while the coherent atom-molecular oscillations coming up soon after the
resonance has been crossed are principally of linear nature. This observation
is supposed to be general for all the nonlinear quantum systems having the same
generic quadratic nonlinearity, due to the basic attributes of the resonance
crossing processes in such systems. The constructed approximation turns out to
have a larger applicability range (than it was initially expected) covering the
whole moderate coupling regime for which the proposed solution accurately
describes all the main characteristics of the system's evolution except the
amplitude of the coherent atom-molecule oscillation, which is rather
overestimated.
