Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
1996-01-19
Nonlinear Sciences
Pattern Formation and Solitons
23 pages, 6 postscript figures, composed using RevTeX. Submitted to PRE
Scientific paper
10.1103/PhysRevE.55.5448
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.
Raitt David
Riecke Hermann
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