Large amplitude plasma waves which can be created by beating two intense laser beams are applicable e.g., to particle acceleration, to induction of plasma currents, and to plasma heating. A central issue in these applications is the nonlinear behaviour of the plasmon. We present a theory model where nonlinear frequency shifts in the plasmon evolution and formation of electromagnetic cascades by inelastic plasmon-photon scattering are accounted. The analytical temporal solution can be constructed in terms of Bessel functions and elliptic integrals. Implications of the results to the applications and further needs to refine the model are discussed. A suggestion for broadening the light spectrum in laserfusion is made.