Localised Radial Patterns on the Free Surface of a Ferrofluid

@article{Hill2021LocalisedRP,
  title={Localised Radial Patterns on the Free Surface of a Ferrofluid},
  author={Dan J. Hill and David J. B. Lloyd and Matthew R. Turner},
  journal={J. Nonlinear Sci.},
  year={2021},
  volume={31},
  pages={79}
}
This paper investigates the existence of localised axisymmetric (radial) patterns on the surface of a ferrofluid in the presence of a uniform vertical magnetic field. We formally investigate all possible small-amplitude solutions which remain bounded close to the pattern’s centre (the core region) and decay exponentially away from the pattern’s centre (the far-field region). The results are presented for a finite-depth, infinite expanse of ferrofluid equipped with a linear magnetisation law… 
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