MODULATED ELECTROMAGNETIC-WAVES IN RELATIVISTIC PLASMAS - FIELD AND KINETIC-EQUATIONS

Modulated electromagnetic plane waves in relativistic, collisionless, unmagnetized plasmas are investigated through expansion in a small par ameter, corresponding to weak dispersion and weak nonlinearity. The os cillation-centre transformation is applied to construct a Hamiltonian action principle for the slow oscillation-centre variables. A descript ion in terms of the relativistic Vlasov equation for oscillation-centr e distribution functions is introduced. A system of coupled field and kinetic equations is obtained order by order. The final result is a ge neralized vector nonlinear Schrodinger equation, with resonant particl e effects included through the coupling to the perturbed Vlasov equati ons.