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 -