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

  • Elementary Particle Physics and Field Theory
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Soviet Physics Journal Aims and scope

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.

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Authors and Affiliations

  1. V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk State University, USSR

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

Authors
  1. V. G. Bagrov
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  2. B. F. Samsonov
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  3. A. V. Shapovalov
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  4. I. V. Shirokov
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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 79–84, May, 1990.

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Bagrov, V.G., Samsonov, B.F., Shapovalov, A.V. et al. Commutative subalgebras of three first-order symmetry operators and separation of variables in the wave equation. Soviet Physics Journal 33, 448–452 (1990). https://doi.org/10.1007/BF00896088

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  • DOI: https://doi.org/10.1007/BF00896088

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