Spatial Dynamics Methods for Solitary Waves on a Ferrofluid Jet
(2018) In Journal of Mathematical Fluid Mechanics 20(4). p.1427-1458- 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,... (More)
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.
(Less)
- author
- Groves, M. D. and Nilsson, D. V. LU
- organization
- publishing date
- 2018
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Mathematical Fluid Mechanics
- volume
- 20
- issue
- 4
- pages
- 32 pages
- publisher
- Birkhäuser Verlag
- external identifiers
-
- scopus:85056763426
- ISSN
- 1422-6928
- DOI
- 10.1007/s00021-018-0370-9
- project
- Nonlinear Water Waves
- language
- English
- LU publication?
- yes
- id
- b0605634-a219-435b-b624-6250f4a64dd1
- date added to LUP
- 2018-11-26 15:17:55
- date last changed
- 2022-04-25 19:24:22
@article{b0605634-a219-435b-b624-6250f4a64dd1,
abstract = {{<p>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.</p>}},
author = {{Groves, M. D. and Nilsson, D. V.}},
issn = {{1422-6928}},
language = {{eng}},
number = {{4}},
pages = {{1427--1458}},
publisher = {{Birkhäuser Verlag}},
series = {{Journal of Mathematical Fluid Mechanics}},
title = {{Spatial Dynamics Methods for Solitary Waves on a Ferrofluid Jet}},
url = {{http://dx.doi.org/10.1007/s00021-018-0370-9}},
doi = {{10.1007/s00021-018-0370-9}},
volume = {{20}},
year = {{2018}},
}