Two-dimensional stationary soliton in a steady hydromagnetic flow

The present paper deals with weakly dispersive hydromagnetic waves of small but finite amplitude propagating slowly (or standing) in a uniform collisionless plasma-flow, which is aligned with an applied magnetic field and the velocity of which is in the specific range so that the system of equations for the steady aligned flow in the ideal magnetohydrodynamics becomes hyperbolic. The two fluid model of the collisionless plasma is used, and by means of the reductive perturbation method, the system is reduced to the Korteweg-de Vries equation expressed in terms of three independent variables which are responsible for slow two-dimensional spatial variation and slower temporal change. Solitons are obtained even without the time dependence, characteristic properties of which are investigated. Boundary conditions to produce the solitons are also examined. (auth.)