Waves in a plasma with Hall dispersion

In a magnetohydrodynamic approximation, an investigation is made of the propagation of waves in a plasma, whose characteristic frequency O is much less than the collision frequency of the electrons ?e-1. It is assumed that the magnetic field is sufficiently strong so that the equality Oe?e»1 will be satisfied, where Oe is the cyclotron frequency of the rotation of the electrons. With large magnetic Reynolds numbers (Rm»1), which are characteristic for many astrophysical problems, this latter condition leads to a need to take account of dispersion effects connected with Hall currents, in the absence of Joule dissipation. The dispersion equation for the propagation of small perturbations is analyzed in the limiting cases of weak dispersion and of a wave propagating along the magnetic field. In the case of weak dispersion, an equation is derived for nonlinear waves. The solutions are found in the form of stationary solitons. The region of such solutions is analyzed. A typical example of a medium with Hall dispersion is an interplanetary plasma, in which the parameter Oe?e is generally great.