Abstract
Linear and nonlinear surface waves on a ferrofluid cylinder surrounding a current-carrying wire are investigated. Suppressing the Rayleigh-plateau instability of the fluid column by the magnetic field of a sufficiently large current in the wire axis-symmetric surface deformations are shown to propagate without dispersion in the long wavelength limit. Using multiple scale perturbation theory, the weakly nonlinear regime may be described by a Korteweg–de Vries equation with coefficients depending on the magnetic field strength. For different values, for the current in the wire hence different solutions such as hump- or hole-solitons may be generated. The possibility to observe these structures in experiments is also elucidated.
Highlights
Solitons are among the most interesting structures in nature
All depending on the magnetic field strength Bo
We have shown that for a sufficiently large current a Korteweg-de Vries equation for axis-symmetric surface distortion can be derived
Summary
Solitons are among the most interesting structures in nature. Being configurations of continuous fields they retain their localized shape even after interactions and collisions. In the present paper we investigate cylindrical solitons of KdV-type on the surface of a ferrofluid in the magnetic field of a current-conducting wire. For a ferrofluid cylinder in the magnetic field of a current-carrying wire the magnetic force may replace gravity and allows for dispersion free surface waves in the long wavelength limit. This in turn paves the way to derive a KdV equation for axis-symmetric surface deformations on the ferrofluid cylinder [11, 12].
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