ON THE PROPERTIES OF AFFINE SOLUTIONS OF COLD PLASMA EQUATIONS

The report will consider affine solutions of the equations of plane oscillations of cold plasma, which, under the assumption of electrostaticity, correspond to the Euler-Poisson equations in the repulsive case. It will also discuss the results obtained in relation to the equilibrium positions (the zero-equilibrium position of the cold plasma equations, both under the assumption of electrostaticity and without it, is unstable in the sense of Lyapunov in the class of all affine solutions), and arbitrary perturbations of an axially symmetric electrostatic solution.