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The derivation of a modified Zakharov–Kuznetsov equation and the stability of its solutions

Published online by Cambridge University Press:  01 September 1999

S. MUNRO  and
E. J. PARKES
S. MUNRO
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, U.K.
E. J. PARKES
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, U.K.
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Abstract

The Zakharov-Kuznetsov equation governs the behaviour of weakly non-linear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. We consider the more realistic situation in which the electrons are non-isothermal. With an appropriate modified form of the electron number density proposed by Schamel, we show that the reductive perturbation procedure leads to a modified Zakharov–Kuznetsov (mZK) equation. The stability of plane-periodic and solitary travelling-wave solutions of the mZK equation to two-dimensional long-wavelength perturbations is investigated using the method of Rowlands and Infeld.

Type
Research Article
Information
Journal of Plasma Physics , Volume 62 , Issue 3 , September 1999 , pp. 305 - 317
Copyright
© 1999 Cambridge University Press

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