Weak Shock Waves in Charged Gas

The problem of plane discontinuities of relatively small amplitude propagating in a layer of nonuniformly charged gas in the variable electric and constant gravity fields is considered within the framework of ideal electrohydrodynamics model. The transport equations of variational nature are derived for their amplitudes and an exact solution of the problem of weak discontinuity is given. Then, the problem of weak shock wave is solved in the approximation to the solution obtained. Examples of propagation of a wave through an arbitrary equilibrium initial state and along a gas layer moving as a solid body in a variable electric field are considered.