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A novel kinetic equation for the spectral function of high-frequency relativistically intense electromagnetic (EM) waves (photon gas) in the presence of a strong magnetic field in a plasma is derived. The spectral function is defined in eight-dimensional coordinates comprising the wave vector and frequency spaces. The nonlinear dynamics of the photon gas for the fully relativistic case is studied by means of the newly derived kinetic equation, and the equations describing the slow motion of plasma under the action of the photon ponderomotive force are obtained. A dispersion relation for relativistic self-modulation of the photon gas with an arbitrary amplitude of the EM waves is derived and new branches for the modulational instability are found. The kinetic equation also yields the fluid equations for the photon gas.
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