Parkes, E.J. and Munro, S. (2005) *The stability of obliquely-propagating solitary-wave solutions to Zakharov-Kuznetsov-type equations.* Journal of Plasma Physics, 71 (5). pp. 695-708. ISSN 0022-3778

## Abstract

In certain circumstances, small amplitude, weakly nonlinear ion-acoustic waves in a magnetized plasma are governed by a Zakharov-Kuznetsov equation or by a reduced form of the equation. Both equations have a plane solitary travelling-wave solution that propagates at an angle αto the magnetic field. The multiple-scale perturbation method developed by Allen and Rowlands is used to calculate the initial growth rate of a small, transverse, long-wavelength perturbation to these solitary-wave solutions. Previous results in the literature are corrected. A numerical determination of the growth rate is given. For k[mid R:] secα[mid R:][double less-than sign]1, where k is the wavenumber of the perturbation, there is excellent agreement between our analytical and numerical results.

Item type: | Article |
---|---|

ID code: | 77 |

Keywords: | solitary-wave solutions, equations, plasma physics, Mathematics, Physics |

Subjects: | Science > Mathematics Science > Physics |

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

Related URLs: | |

Depositing user: | Miss Jacqueline Miller |

Date Deposited: | 19 Dec 2005 |

Last modified: | 04 Oct 2012 11:57 |

URI: | http://strathprints.strath.ac.uk/id/eprint/77 |

### Actions (login required)

View Item |