A bidirectional wave transformation of the cold plasma equations

The bidirectional wave transformation developed for scalar equations is shown to have interesting extensions for first-order hyperbolic systems. Assuming a localized waveform of the solution gives an equation for the envelope of the localized wave. The type of the envelope equation depends on the characteristics of the original hyperbolic equations, and the speed of the localized wave. This method is applied to the cold plasma equations. In the general case integral representations are found for the fundamental solutions; and in a special case, exact solutions are constructed.