The Maximally-Efficient Generation Approach (MEGA) for an oto-dynamo i
s investigated based on the simplest model of the Parker Migratory Dyn
amo. The a-effect is supposed inhomogeneous. The equations which gover
n the magnetic field are solved with the use of a WKB method. Turning
points and the behavior of the solution in their vicinity are derived.
The point of maximum dynamo wave amplitude is shown to be shifted fro
m the point where the generation sources are maximum towards the direc
tion of the dynamo wave propagation. For the solar dynamo the obtained
direction of the dynamo wave propagation reverses over the subpolar d
omains. Dynamo waves with a poleward migration are observable over the
polar regions of the Sun. The generation threshold is calculated. The
properties of the dynamo waves are compared with observational data f
or the solar cycle. An asymptotic solution for oscillating modes of th
e galactic disk dynamo is also obtained.