Published online by Cambridge University Press: 13 March 2009
In this paper we consider relativistic interaction of an overdense plasma with very intense electromagnetic waves. Nonlinear coupling of dispersive waves in the presence of an ambient magnetic field is investigated. Lorentz transformation together with rotations of the co-ordinate system are employed to obtain analytic solutions. Two cases with variable gamma factors are treated in detail: in one case the magnitude of the electric field remains constant in the transformed frame; in the other no restriction is made to the electric field, but the total stream velocity vanishes in the transformed frame. Numerical illustrations of various modes for these two cases are depicted graphically.