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A theory of the nonlinear plasma waves in graphene is developed in thenonperturbative regime. The influence of strong electric fields on the positionand linewidth of plasma resonances in the far-infrared transmissionexperiments, as well as on the wavelength and the propagation length in thescanning near-field optical microscopy experiments is studied. The theory showsthat the fields of order of a few to a few tens of kV/cm should lead to a redshift and broadening of plasma resonances in the first type and to a reductionof the wavelength and the propagation length in the second type of experiments.

Influence of optical nonlinearities on plasma waves in graphene