One-dimensional, weakly-nonlinear electromagnetic solitary waves in a plasma

Summary form only given. The properties of one-dimensional, weakly nonlinear electromagnetic solitary waves in a plasma have been investigated. Consideration is given to the regime in which the electrons are weakly relativistic, the solitary wave speed is close to the velocity of light c, the electron temperature is negligible because the directed motion of the electrons is assumed to be much larger than the thermal motion, and the ion motion is negligible because the pulse length l is sufficiently short to satisfy /spl omegasub /spl pil/c /spl Lt/ 1, where /spl omegasub /spl pi is the ion plasma frequency. The solution of the resulting eigenvalue problem shows that the solitary waves have amplitudes which are allowed discrete values only. Higher-order solitary waves, whose vector potential envelope is highly oscillatory, are shown to consist, in the group velocity frame, of two trapped, oppositely traveling waves. Simple closed-form solutions have been obtained for higher-order solitary waves.