We derive the kinetic equation governing the evolution of the action density of a wave propagating in a weakly nonuniform, nonstationary medium characterized by fluctuations that are small in magnitude (but need not be slowly varying). The method of derivation is based on the Weyl representation of a general linear wave equation, which leads to a natural definition of the wave-action density and an analysis rooted in the ray phase space. The result is thus a classical wave derivation of the radiation transport equation for a general scalar wave equation. We illustrate our derivation with three example wave equations governing propagation in fluctuating media.
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Steven W. McDonald (1991) studied this question.
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