Abstract
We discuss the question whether the way of finding the conservation laws based on variational formalism is applicable to the multilevel problems of radiative transfer in a homogeneous atmosphere. For expository reasons, the simplest one-dimensional model case is considered. For the special three-level problem treated in the paper the Lagrangian approach allows one to derive not only the H- and K-integrals, but also the nonlinear integral which is an analog of the Q-integrals previously obtained for the classical transfer problems. It is shown that, in general, the constraints imposed by the variational principle on the symmetry properties of the transfer equations are too stringent to be satisfied.
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Translated from Astrofizika, Vol. 42, No. 2, pp. 235–252, April–June, 1999.
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Nikoghossian, A.G., Krikorian, R.A. Conservation laws for multilevel transfer problems. Astrophysics 42, 201–205 (1999). https://doi.org/10.1007/BF02711606
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DOI: https://doi.org/10.1007/BF02711606