Journal of Plasma Physics



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


S. MUNRO a1 and E. J. PARKES a1
a1 Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, U.K.

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.

(Received November 20 1998)
(Revised April 22 1999)