  A dynamical scheme of quantization of symplectic manifolds is described. It
is based on intrinsic Schr\"odinger and Heisenberg type nonlinear evolutionary
equations with multidimensional time running over the manifold. This is the
restricted version of the original article to be published in ``Asymptotic
Methods for Wave and Quantum Problems'' (M. Karasev, ed.), Advances in Math.
Sci., AMS.
