  It is well known that the Gaussian wave packet dynamics can be written in
terms of Hamilton equations in the extended phase space that is twice as large
as in the corresponding classical system. We construct several generalizations
of this approach that include non-Gausssian wave packets. These generalizations
lead to the further extension of the phase space while retaining the Hamilton
structure of the equations of motion. We compare the Gaussian dynamics with
these non-Gaussian extensions for a particle with the quartic potential.
