Invariant imbedding and searchlight problem in turbid slab (Q1179353)

It is shown how to get analytically an initial-value solution of the scattering function in the searchlight problem which concerns the reflection of a narrow collimated beam, on the top of a vertically inhomogeneous and anisotropically scattering atmosphere, by the terrestrial surface. For the searchlight an invariant imbedding results in a Cauchy system of the scattering function in the Riccati-type of a nonlinear integro- differential equation with the initial condition. The mathematical model is constructed with large computer calculations and approximations.