Symmetry and solution of neutron transport equations in nonhomogeneous media. (English) Zbl 1474.35044

Tsyfra, Ivan; Czyżycki, Tomasz

Abstr. Appl. Anal. 2014, Article ID 724238, 9 p. (2014).

Summary: We propose the group-theoretical approach which enables one to generate solutions of equations of mathematical physics in nonhomogeneous media from solutions of the same problem in a homogeneous medium. The efficiency of this method is illustrated with examples of thermal neutron diffusion problems. Such problems appear in neutron physics and nuclear geophysics. The method is also applicable to nonstationary and nonintegrable in quadratures differential equations.

MSC:

35A30	Geometric theory, characteristics, transformations in context of PDEs
58J72	Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds

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