Munro, S. and Parkes, E.J.
(2000)
*Stability of solitary-wave solutions to a modified Zakharov-Kuznetsov equation.*
Journal of Plasma Physics, 64 (4).
pp. 411-426.
ISSN 0022-3778

## Abstract

In the context of ion-acoustic waves in a magnetized plasma comprising cold ions and non-isothermal electrons, small-amplitude, weakly nonlinear waves have been shown previously by Munro and Parkes to be governed by a modified version of the Zakharov-Kuznetsov equation. In this paper, we consider solitary travelling-wave solutions to this equation that propagate along the magnetic field. We investigate the initial growth rate [gamma](k) of a small transverse sinusoidal perturbation of wavenumber k. The instability range is shown to be 0 < k < 3. We use the multiple-scale perturbation method developed by Allen and Rowlands to determine a consistent expansion of [gamma] about k = 0 and k = 3. By combining these results in the form of a Padæ#169; approximant, an analytical expression for [gamma] is found that is valid for 0 < k < 3. [gamma] is also determined by using the variational method developed by Bettinson and Rowlands. The two results for [gamma] are compared with a numerical determination.

Item type: | Article |
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ID code: | 78 |

Keywords: | Physics, Condensed Matter Physics |

Subjects: | Science > Physics |

Department: | Faculty of Science > Mathematics and Statistics Unknown Department |

Depositing user: | Miss Jacqueline Miller |

Date Deposited: | 19 Dec 2005 |

Last modified: | 20 Oct 2015 10:58 |

URI: | http://strathprints.strath.ac.uk/id/eprint/78 |

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