Exact solution of the transport equation for imperfect Rayleigh scattering in a semi-infinite atmosphere

Details Exact solution of the transport equation for imperfect Rayleigh scattering in a semi-infinite atmosphere Exact solution of the transport equation for imperfect Rayleigh scattering in a semi-infinite atmosphere

May 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979ap%26ss..62..143d&link_type=abstract

Astrophysics and Space Science, vol. 62, no. 1, May 1979, p. 143-147.

Mathematics

Atmospheric Scattering, Matrices (Mathematics), Radiative Transfer, Rayleigh Scattering, Boundary Conditions, Boundary Value Problems, Differential Equations, Integral Equations, Laplace Transformation, Wiener Hopf Equations

Scientific paper

By performing the one-sided Laplace transform on the matrix integro-differential equation for a semi-infinite plane parallel imperfect Rayleigh scattering atmosphere we derive an integral equation for the emergent intensity matrix. Application of the Wiener-Hopf technique to this integral equation will give the emergent intensity matrix in terms of singular H-matrix and an unknown matrix. The unknown matrix has been determined considering the boundary condition at infinity to be identical with the asymptotic solution for the intensity matrix.

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