Nonlinear modulation of spatial waves in a steady plasma flow

Nonlinear modulation of strongly dispersive ion-acoustic standing waves produced by some obstacle in a uniform plasma flow, is investigated by means of the reductive perturbation method. The two fluid equations composed of cold ions and isothermal electrons are used, which in the specific ranges of Mach number and wavenumber permit the spatial waves. Consequently, the system is reduced to the nonlinear Schroedinger equation expressed in terms of three independent variables which are responsible for slow two-dimensional spatial variation and slower temporal change. It is further shown that in general the nonlinear Schroedinger equation derived from the Korteweg-de Vries equation is always stable as to the modulational instability. (auth.)