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Two-dimensional surface waves in magnetohydrodynamics
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Hunt, Matthew (2019) Two-dimensional surface waves in magnetohydrodynamics. Journal of Plasma Physics, 85 (4). 905850405. doi:10.1017/S0022377819000497 ISSN 0022-3778.
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Official URL: https://doi.org/10.1017/S0022377819000497
Abstract
The study of nonlinear waves in water has a long history beginning with the seminal paper by Korteweg & de Vries (Phil. Mag., vol. 39, 1895, p. 240) and more recently for magnetohydrodynamics Danov & Ruderman (Fluid Dyn., vol. 18, 1983, pp. 751–756). The appearance of a Hilbert transform in the nonlinear equation for magnetohydrodynamics (MHD) distinguishes it from the water wave model description. In this paper, we are interested in examining weakly nonlinear interfacial waves in dimensions. First, we determine the wave solution in the linear case. Next, we derive the corresponding generalisation for the Kadomtsev–Petviashvili (KP) equation with the inclusion of an equilibrium magnetic field. The derived governing equation is a generalisation of the Benjamin–Ono (BO) equation called the Benjamin equation first derived in Benjamin (J. Fluid Mech., vol. 245, 1992, pp. 401–411) and in the higher-dimensional context in Kim & Akylas (J. Fluid Mech., vol. 557, 2006, pp. 237–256).
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Engineering > WMG (Formerly the Warwick Manufacturing Group) |
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| Journal or Publication Title: | Journal of Plasma Physics | ||||||
| Publisher: | Cambridge University Press | ||||||
| ISSN: | 0022-3778 | ||||||
| Official Date: | 15 July 2019 | ||||||
| Dates: |
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| Volume: | 85 | ||||||
| Number: | 4 | ||||||
| Article Number: | 905850405 | ||||||
| DOI: | 10.1017/S0022377819000497 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Journal of Plasma Physics http://doi.org/10.1017/S0022377819000497. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder. | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 21 June 2019 | ||||||
| Date of first compliant Open Access: | 15 January 2020 | ||||||
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