A simple example of a nonlinear problem of reflection and transmission of radiation by a one-dimensional scattering and absorbing isotropic medium of finite geometric thickness with conservative and isotropic scattering is examined. The effectiveness of the linear images (LI) method developed previously by the author for solving nonlinear radiative transfer problems is demonstrated. An explicit expression is obtained for the desired LI. It is used to obtain a solution of the reflection and transmission problem for two-sided illumination of a medium of finite thickness in explicit closed form and the radiation field inside it is determined for two mutually opposite statements of the problem: “direct” and “inverse.” Numerical results are given illustrating the difference between the solutions of these problems in the linear and nonlinear cases.
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H. V. Pikichyan, Astrophysics 53, 251 (2010).
H. V. Pikichyan, Astrophysics 59, 114 (2016).
H. V. Pikichyan, Astrophysics 59, 272 (2016).
H. Pikichian, in: J. J. Carrol and T. A. Goldman, eds. Proc. of international conf. on “Lasers’97" (New Orleans, LA, December 15-19, 1997), pp. 226-232, STS press, McLean, VA (1998), 1011 pp.
H. V. Pikichian, in: H. Harutyunian, A. Mickaelian, and Y. Terzian, eds., Proc. of the Conf. “Evolution of Cosm. Obj. through their Phys. Activity” (dedicated to V. Ambartsumian’s 100th anniversary, 15-18 Sept. 2008 Yerevan-Byurakan, Armenia), pp. 302-315, Publ. House of NAS RA, Yerevan (2010), 356 pp.
V. A. Ambartsumyan, Izv. AN Arm. SSR, Estestv. nauki, No. 1-2, pp. 31-36 (1944).
V. A. Ambartsumyan, DAN Arm. SSR 38(4), 225-230 (1964).
V. A. Ambartsumyan, in: V. V. Sobolev, et al, eds., Theory of Stellar Spectra, pp. 91-104, Nauka, Moscow (1966), 388 pp.
H. V. Pikichyan, JQSRT 183, 113 (2016).
H. V. Pikichyan, in: Fifth Russ.-Arm. Conf. on Math-phys., Complex analysis and related questions, Abstracts of talks, pp. 48-49 (Sep. 28-Oct. 3, 2014, Erevan, Armenia), Izd. NAN RA, Erevan (2014), 56 pp.
H. V. Pikichyan, in: A. M. Mickaelian, H. A. Harutyunian, and E. H. Nikoghosyan, ed., “Non-Stable Universe: Energetic Resources, Activity Phenomena, and Evolutionary Processes”, Proc. of Intern. Symp. dedicated to the 70th anniversary of the BAO, pp. 231-237, Sept. 19-23, 2016, Yerevan-Byurakan, Armenia, ASP Conference Series, 511, Astron. Soc. Pacif. , San Francisco (2017), 314 pp.
H. V. Pikichyan, in: V. P. Grinin, H. Harutyunian, V. B. Il’in, A. F. Kholtygin, and A. Nioghossian, eds., Radiation mechanisms of astrophysical objects: classics today, pp. 65-72, Proc. of the conf. in honor of the 100th birthday of Academician V. V. Sobolev (St. Petersburg, Sept. 21-25 (2015), Publ. comp. “Edit Print”, Yerevan (2017), 460 pp.
H. V. Pikichyan, in: Seventh Russ.-Arm. Conf. on Math-phys., Complex analysis and related questions, Abstracts of talks, pp. 64-67 (Sept. 9-15, 2018, Erevan, Armenia), Izd.”Gitutyun,” Erevan (2018), 84 pp.
H. V. Pikichyan, report in Conf. “Instability Phenomena and Evolution of the Universe”, devoted to Viktor Ambartsumian’s 110th anniversary, (Byurakan Astrophysical Observatory, Armenia, Sept 17-21, 2018. To be published in Comm. of BAO.
V. V. Ivanov, Radiative Transfer and Spectra of Celestial Objects [in Russian], Nauka, Moscow (1969), 472 pp.
V. A. Ambartsumyan, DAN Arm. SSSR 39, 159 (1964).
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Translated from Astrofizika, Vol. 62, No. 3, pp. 437-450 (August 2019)
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Pikichyan, H.V. Analytic Solution of the Nonlinear Radiative Diffusion Problem in a One-Dimensional Purely Scattering Medium. I. Astrophysics 62, 387–401 (2019). https://doi.org/10.1007/s10511-019-09590-7
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DOI: https://doi.org/10.1007/s10511-019-09590-7