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Derivation of a novel kinetic equation for the spectral function of
hich frequency relativistically intense electromagnetic (EM) waves
(photon gas) is presented. In the kinetic equation appears an additional term,
and the spectral function is defined in seven-dimensional coordinate, wave
vector and frequency space. Nonlinear dynamics of the photon gas-plasma
in the fully relativistic case is studied by the new kinetic equation
and equations describing the slow motion of a plasma under the action of a
ponderomotive force. A general dispersion relation for an arbitrary amplitude
EM wave is derived and new branches for the modulational instability are
found. Adiabatic photon capture in a well with an arbitrary plasma-well
profile is investigated.
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