Solutions of the kinetic equation for a collisionless plasma in an external electromagnetic field

The only existing exact solution of Cauchy's problem for kinetic equation (KE) is obtained for relativistic collisionless plasma in the strong field of a plane electromagnetic wave with an arbitrary polarization. Various methods of iterative solution of KE are compared. The formal solution of KE is obtained for plasma in the presence of magnetic field along which the wave is spreading. This solution provides a basis for obtaining approximate as well as exact solutions in various particular cases.