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

Abstract

Surface waves on ferrofluids exposed to a dc-magnetic field exhibit a non-monotonic 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.

23 pages, 6 postscript figures, composed using RevTeX. Submitted to PRE

References in corpus (2)

• Domain Structures in Fourth-Order Phase and Ginzburg-Landau Equations
• Temporal Forcing of Small-Amplitude Waves in Anisotropic Systems

Cited by in corpus (5)

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• Parametrically excited surface waves in magnetic fluids: observation of domain structures
• Localised patterns in a generalised Swift--Hohenberg equation with a quartic marginal stability curve
• Holes and chaotic pulses of traveling waves coupled to a long-wave mode