On the symmetries of many-component Vlasov-Poisson-Ampere plasmas

For investigation of the symmetry of the systems of the Vlasov-Poisson-Ampere equations the method of Lie group developed by Ovsiannikov is available. It is shown that this system of equations admits the continuous group of transformations and the infinitesimal generators of this group are constructed. The results obtained indicate that for many-component plasma there are no solutions which correspond to electrostatic oscillations. They contradict the results derived by Taranov for a one-component plasma. 3 refs. (author)