  This paper presents existence theories for several families of axisymmetric
solitary waves on the surface of an otherwise cylindrical ferrofluid jet
surrounding a stationary metal rod. The ferrofluid, which is governed by a
general (nonlinear) magnetisation law, is subject to an azimuthal magnetic
field generated by an electric current flowing along the rod.
  The ferrohydrodynamic problem for axisymmetric travelling waves is formulated
as an infinite-dimensional Hamiltonian system in which the axial direction is
the time-like variable. A centre-manifold reduction technique is employed to
reduce the system to a locally equivalent Hamiltonian system with a finite
number of degrees of freedom, and homoclinic solutions to the reduced system,
which correspond to solitary waves, are detected by dynamical-systems methods.
