Propagation of fast ion-acoustic waves in multi-dimensions

By using a perturbation method, it is shown that the nonlinear fast ion-acoustic wave of a small but finite amplitude in a collisionless plasma consisting of hot and isothermal electrons and cold ions is governed by a nonlinear equation in which, in general, the coefficients of nonlinear and dispersive terms are not constant but depend on the form of the wave-front and the lowest order term contains mean curvature of the wave-front as its coefficient.