### 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.

Original language | English |
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Pages (from-to) | 377-381 |

Number of pages | 5 |

Journal | Soviet Physics Journal |

Volume | 34 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 1991 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Soviet Physics Journal*,

*34*(4), 377-381. https://doi.org/10.1007/BF00898108

**Complete sets of symmetry operators containing a second-order operator and the problem of separation of variables in the wave equation.** / Bagrov, V. G.; Samsonov, B. F.; Shapovalov, A. V.; Shirokov, I. V.

Research output: Contribution to journal › Article

*Soviet Physics Journal*, vol. 34, no. 4, pp. 377-381. https://doi.org/10.1007/BF00898108

}

TY - JOUR

T1 - Complete sets of symmetry operators containing a second-order operator and the problem of separation of variables in the wave equation

AU - Bagrov, V. G.

AU - Samsonov, B. F.

AU - Shapovalov, A. V.

AU - Shirokov, I. V.

PY - 1991/4

Y1 - 1991/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34249918594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249918594&partnerID=8YFLogxK

U2 - 10.1007/BF00898108

DO - 10.1007/BF00898108

M3 - Article

AN - SCOPUS:34249918594

VL - 34

SP - 377

EP - 381

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 4

ER -