Exact solutions to a steady-state radiation-transfer equation in one-dimensional planar and spherical geometries (Q1975083)

The author proposes new exact solutions to a steady-state equation of radiation transfer with anisotropic scattering for one-dimensional planar and spherical geometries and exact solutions of another form of such an equation. Questions of nonunique representation of all solutions to this equation are considered and their smoothness analyzed. Exact solutions are also constructed in the form of series by the proposed exact analytical solutions. These solutions differ from the known exact solutions. The solutions obtained can be used as test solutions in numerically solving direct and inverse problems of the radiation-transfer theory and the dynamics of a radiating gas in one-dimensional planar and spherical geometries.