On the nonuniqueness of solutions for nonlinear integral equations in radiative transfer theory

Details On the nonuniqueness of solutions for nonlinear integral equations in radiative transfer theory On the nonuniqueness of solutions for nonlinear integral equations in radiative transfer theory

Apr 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984jqsrt..31..285d&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer (ISSN 0022-4073), vol. 31, April 1984, p. 285-299.

Physics

7

Integral Equations, Isotropic Media, Nonlinear Systems, Polarized Light, Radiative Transfer, Eigenvectors, Heuristic Methods, Invariance, Iterative Solution, Uniqueness Theorem

Scientific paper

The nonuniqueness problem is considered for the nonlinear integral equations satisfied by the reflection and transmission matrices of homogeneous plane-parallel atmospheres. The analysis of the problems for semi-infinite and finite atmospheres is based on a recently developed biorthogonality concept. Explicit expressions for nonphysical solutions are derived. The structure of these solutions reveals that iterative solution procedures may easily yield nonphysical results, if no proper attention is paid to certain linear constraints.

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