Abstract
For the wave equation in Minkowski space, a space is defined of nontrivial local second-order differential symmetry operators. The algebraic conditions, which, in accordance with the general theorems on the separation of variables, must be satisfied by the commutative subalgebras, including two first-order operators and second-order operator, are formulated in coordinate-free form. On the basis of these subalgebras, there are obtained all the complete sets of symmetry operators of types (2.0), (2.1). Sets are presented which do not have analogues in papers of other authors.
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E. G. Kalnins and W. Miller, Jr., J. Math. Phys.,18, 271 (1977).
E. G. Kalnins and W. Miller, Jr., J. Math. Phys.,19, 1233 (1978).
E. G. Kalnins and W. Miller, Jr., J. Math. Phys.,19, 1247 (1978).
V. N. Shapovalov, Differents Uravn.16, 1864 (1980).
V. G. Bagrov et al., Preprint No. 31, Theoretical Physics, Siberian Section of the Academy of Sciences of the USSR, Tomsk (1989).
V. G. Bagrov et al., Preprint No. 38, Theoretical Physics, Siberian Section of the Academy of Sciences of the USSR, Tomsk (1989).
A. V. Shapovalov and I. V. Shirokov, in: Contemporary Group Analysis. Methods and Applications [in Russian], Leningrad (1990), pp. 52–58.
V. G. Bagrov et al., Grav. Elektromagn., No. 4, 20–23, Minsk (1989).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 115–119, April, 1991.
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Bagrov, V.G., Samsonov, B.F., Shapovalov, A.V. et al. Complete sets of symmetry operators containing a second-order operator and the problem of separation of variables in the wave equation. Soviet Physics Journal 34, 377–381 (1991). https://doi.org/10.1007/BF00898108
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DOI: https://doi.org/10.1007/BF00898108