Cylindrical Korteweg–de Vries solitons on a ferrofluid surface

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.