  We present a rigorous analysis of the generalized Landau-Zener problem for
the two-level interacting Bose-Einstein condensates. We show that the dynamics
of the system is accurately, in detail, described by a two-term variational
ansatz that is valid for the whole time domain and is applicable for any set of
involved parameters. Applying an exact third order nonlinear differential
equation we construct an advanced fifth order polynomial equation for the final
transition probability serving as a highly accurate generalized Landau-Zener
formula.
