A kinetic model for the one-dimensional electromagnetic solitons in an isothermal plasma

Two nonlinear second order differential equations for the amplitude of the vector potential and for the electrostatic potential are derived, starting from the full Maxwell equations where the field sources are calculated by integrating in the momentum space the particle distribution function, which is an exact solution of the relativistic Vlasov equation. The resulting equations are exact in describing a hot one- dimensional plasma sustaining a relativistically intense, circularly polarized electromagnetic radiation. The case of standing soliton-like structures in an electron–positron plasma is then investigated. It is demonstrated that at ultrarelativistic temperatures extremely large amplitude solitons can be formed in a strongly overdense plasma.