On a kinetic approach to the modulational stability of envelope solitons in a relativistic plasma in an external electric field

Summary The formation of envelope solitons is discussed in a relativistic plasma under the influence of a fluctuating electric field. We use the kinetic-theory approach for our analysis. Due to the larger inertia, only the electrons are considered to be relativistic and the ions to be nonrelativistic. A NLS equation is derived describing the motion of the solitary wave. This NLS equation actually comes from an approximation of a pair of equations which can be considered to be a relativistic generalisation of the Zakharov equation. We next discuss the exact form of the envelope solitary-wave solution of the NLS equation and the modulation stability of such a wave. When the density, momentum and energy of such wave packets are fixeda priori, conditions are derived for the parameters of the problem from such stability consideration.