Large amplitude electron plasma oscillations

•Two generic coupled equations are derived.•Threshold values for parametric instabilities are deduced.•The coupled equations are studied numerically in the strongly nonlinear regime.

We consider a cold plasma in order to find new large-amplitude wave solutions in the long-wavelength limit. Accordingly we derive two generic coupled equations which describe the energy exchange between the electrostatic and electromagnetic waves. A new kind of quasi-periodic behavior is found. Our derivations may be considered as a prerequisite to extended studies of stimulated Raman scattering for cases where the wave amplitudes are so large that standard perturbation techniques are not applicable.