Commutative subalgebras of three first-order symmetry operators and separation of variables in the wave equation

V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, I. V. Shirokov

Research output: Contribution to journalArticle

Abstract

The problem of complex separation of variables in the wave equation is considered in four-dimensional Minkowskii space-time. In contrast to the known series of researches by Kalnins and Miller (see Ref. Zh., Fiz., 2B9 (1978); 1B208 and 1B209 (1979), e.g.), underlying this research is a theorem on the necessary and sufficient conditions of total separation of variables in the non-parabolic V. N. Shapovalov equation (Differents. Uravn., 16, No. 10, 1864-1874 (1980)). Nonequivalent complete sets of three differential first-order symmetry operators are constructed, appropriate coordinate systems are found, and complete separation of variables is performed in the wave equation.

Original languageEnglish
Pages (from-to)448-452
Number of pages5
JournalSoviet Physics Journal
Volume33
Issue number5
DOIs
Publication statusPublished - May 1990
Externally publishedYes

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wave equations
operators
symmetry
theorems

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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Commutative subalgebras of three first-order symmetry operators and separation of variables in the wave equation. / Bagrov, V. G.; Samsonov, B. F.; Shapovalov, A. V.; Shirokov, I. V.

In: Soviet Physics Journal, Vol. 33, No. 5, 05.1990, p. 448-452.

Research output: Contribution to journalArticle

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