Nonlinear equations in linear problems of radiation transfer in plane atmospheres

Astronomy and Astrophysics – Astronomy

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Atmospheric Radiation, Atmospheric Scattering, Nonlinear Equations, Radiative Transfer, Atmospheric Models, Frequency Distribution, Radiation Sources, Roots Of Equations

Scientific paper

Rybicki (1977) has established that, besides the generally known integrals that are linear with respect to intensity (I), the equation of radiative transfer also has certain integrals that are quadratic with respect to I. This paper shows that, by starting from Rybicki's basic idea, more general equations that are bilinear with respect to I can be obtained. Attention is restricted to the simplest case of isotropic scattering without a change in frequency. Generalizations to anisotropic scattering and to scattering in line frequencies with complete frequency redistribution are briefly discussed.

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