The Korteweg-de Vries-Zakharov-Kuznetsov equation for electron-acoustic waves

Motivated by a recent paper [Phys. Plasmas 7, 2987 (2000)] highlighting the potential importance of the electron-acoustic wave in interpreting the solitary waves observed by high time resolution measurements of the electric field in the auroral region, the effect of a magnetic field on weakly nonlinear electron-acoustic waves is investigated. A Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equation is derived for a plasma comprised of cool and hot electrons and a species of fluid ions. Two models are employed for the ions: magnetized and unmagnetized. When the ions are magnetized the frequency constraints imposed upon the electron-acoustic wave packet prove to be too limiting to be of general use. The second model, which treats the ions as a stationary neutralizing background, overcomes the restrictions imposed by the former and is more fitting for the frequency domain of the electron-acoustic wave. Plane and ellipsoidal soliton solutions are admitted by the KdV-ZK equation, the latter perhaps able to explain some of the two dimensional features of the solitary waves observed in the Earth's high altitude auroral region. Both models for the ions predict only negative potential solitons. It is discussed how the plasma model might be adapted to produce positive potential solitons. (C) 2001 American Institute of Physics.