### 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 language | English |
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Pages (from-to) | 448-452 |

Number of pages | 5 |

Journal | Soviet Physics Journal |

Volume | 33 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1990 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Soviet Physics Journal*,

*33*(5), 448-452. https://doi.org/10.1007/BF00896088