A kinematic alpha omega-dynamo model of magnetic field generation in a
thin convection shell with nonuniform helicity for large dynamo numbe
rs is considered in the framework of Parker's migratory dynamo. The as
ymptotic solution obtained of equations governing the magnetic field h
as the form of an anharmonic travelling dynamo wave. This wave propaga
tes over most latitudes of the solar hemisphere from high latitudes to
the equator, and the amplitude of the magnetic field first increases
and then decreases with propagation. Over the subpolar latitudes. the
dynamo wave reverses; there the dynamo wave propagates polewards and d
ecays with latitude. The half-width of the maximum of the magnetic fie
ld localisation and the phase velocity of the dynamo wave are calculat
ed. Butterfly diagrams are plotted and analysed and these show that ev
en a simple model may reveal some properties of the solar magnetic fie
lds.