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Spatial Dynamics Methods for Solitary Waves on a Ferrofluid Jet

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Abstract

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.

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Authors and Affiliations

  1. Fachrichtung Mathematik, Universität des Saarlandes, Postfach 151150, 66041, Saarbrücken, Germany

    M. D. Groves

  2. Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK

    M. D. Groves

  3. Centre for Mathematical Sciences, Lund University, PO Box 118 , 22100, Lund, Sweden

    D. V. Nilsson

Authors
  1. M. D. Groves
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  2. D. V. Nilsson
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Correspondence to M. D. Groves.

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Communicated by G. Iooss.

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Groves, M.D., Nilsson, D.V. Spatial Dynamics Methods for Solitary Waves on a Ferrofluid Jet. J. Math. Fluid Mech. 20, 1427–1458 (2018). https://doi.org/10.1007/s00021-018-0370-9

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