Groups of equivalency in the problems of neutron diffusion within heterogeneous medium
DOI:
https://doi.org/10.24028/gzh.0203-3100.v32i3.2010.117537Abstract
An application of group equivalence transformations for generating solutions of neutron diffusion equation in heterogeneous medium from solutions for homogeneous medium is studied. The problem of equivalency of partial differential equations is also discussed.References
Бенурц К., Виртц К. Нейтронная физика. - Москва: Атомиздат, 1968. - 456 с.
Козачок И. А., Цифра И. М. Теоретико-групповой анализ физических полей в градиентно-неоднородных средах и его применение в проблеме диффузии тепловых нейтронов // Геофиз. журн. - 2004. - 26, № 2. - С. 122-127.
Овсянников Л. В. Групповой анализ дифференциальных уравнений. - Москва: Наука, 1978. - 399 с.
Олвер П. Приложения группы Ли к дифференциальным уравнениям. - Москва: Мир, 1989. - 639 с.
Цифра I. М. Симетрійна редукція диференціальних рівнянь в частинних похідних з двома незалежними змінними // 36. праць Ін-ту математики НАН України. - 2006. - 3, № 2. - С. 309-315.
Fushchich W. I., Tsifra I. M. On a reduction and solutions of the nonlinear wave equations with broken symmetry // J. Phys. A: Math. Gen. - 1987. - 20. - L45-L48.
Levi D., Winternitz P. Nonclassical symmetry reduction: example of the Bussinesg equation symmetry // J. Phys. A: Math. Gen. - 1989. - 22, № 15. - P. 2915-2924.
Tsyfra I. M. Symmetry reduction of nonlinear differential equations // Proc. Inst. Math. NAS of Ukraine. - Kiev. - 2004. - 50. - P. 266-270.
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