Parametric Forcing of Waves with Non-Monotonic Dispersion Relation: Domain Structures in Ferrofluids?

Surface waves on ferrofluids exposed to a dc-magnetic field exhibit a nonmonotonic dispersion relation. The effect of a parametric driving on such waves is studied within suitable coupled Ginzburg-Landau equations. Due to the non-monotonicity the neutral curve for the excitation of standing waves can have up to three minima. The stability of the waves with respect to long-wave perturbations is determined via a phase-diffusion equation. It shows that the band of stable wave numbers can split up into two or three sub-bands. The resulting competition between the wave numbers corresponding to the respective sub-bands leads quite naturally to patterns consisting of multiple domains of standing waves which differ in their wave number. The coarsening dynamics of such domain structures is addressed. February 9, 2008 05.45.+b, 05.90.+m, 47.20. Tg Typeset using REVTEX 1