TY - JOUR

T1 - Commutative subalgebras of three first-order symmetry operators and separation of variables in the wave equation

AU - Bagrov, V. G.

AU - Samsonov, B. F.

AU - Shapovalov, A. V.

AU - Shirokov, I. V.

PY - 1990/5

Y1 - 1990/5

N2 - 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.

AB - 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.

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U2 - 10.1007/BF00896088

DO - 10.1007/BF00896088

M3 - Article

AN - SCOPUS:34249922830

VL - 33

SP - 448

EP - 452

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 5

ER -