  The Rosensweig instability has a special character among the frequently
discussed instabilities. One distinct property is the necessary presence of a
deformable surface, and another very important fact is, that the driving force
acts purely via the surface and shows no bulk effect. These properties make it
rather difficult to give a correct weakly nonlinear analysis. In this paper we
give a detailed derivation of the appropriate amplitude equation based on the
hydrodynamic equations emphasizing the conceptually new procedures necessary to
deal with the distinct properties mentioned above. First the deformable surface
requires a fully dynamic treatment of the instability and the observed
stationary case can be interpreted as the limiting case of a frozen-in
characteristic mode. Second, the fact that the driving force is manifest in the
boundary conditions, only, requires a considerable change in the formalism of
weakly nonlinear bifurcation theory. To obtain the amplitude equations a
combination of solubility conditions and (normal stress) boundary conditions
has to be invoked in all orders of the expansions.
