### Abstract

A method of noncommutative integration of linear partial differential equations that is analogous to noncommutative integration of finite-dimensional Hamiltonian systems is proposed. The method is based on the concept, introduced in the paper, of a λ representation of Lie algebras. The method can be applied to the integration of the Klein-Gordon equation in Riemannian spaces of non-Stäckel type (i.e., in spaces that do not admit complete separation of the variables).

Original language | English |
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Pages (from-to) | 921-934 |

Number of pages | 14 |

Journal | Theoretical and Mathematical Physics |

Volume | 104 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1995 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

*Theoretical and Mathematical Physics*,

*104*(2), 921-934. https://doi.org/10.1007/BF02065973

**Noncommutative integration of linear differential equations.** / Shapovalov, A. V.; Shirokov, I. V.

Research output: Contribution to journal › Article

*Theoretical and Mathematical Physics*, vol. 104, no. 2, pp. 921-934. https://doi.org/10.1007/BF02065973

}

TY - JOUR

T1 - Noncommutative integration of linear differential equations

AU - Shapovalov, A. V.

AU - Shirokov, I. V.

PY - 1995

Y1 - 1995

N2 - A method of noncommutative integration of linear partial differential equations that is analogous to noncommutative integration of finite-dimensional Hamiltonian systems is proposed. The method is based on the concept, introduced in the paper, of a λ representation of Lie algebras. The method can be applied to the integration of the Klein-Gordon equation in Riemannian spaces of non-Stäckel type (i.e., in spaces that do not admit complete separation of the variables).

AB - A method of noncommutative integration of linear partial differential equations that is analogous to noncommutative integration of finite-dimensional Hamiltonian systems is proposed. The method is based on the concept, introduced in the paper, of a λ representation of Lie algebras. The method can be applied to the integration of the Klein-Gordon equation in Riemannian spaces of non-Stäckel type (i.e., in spaces that do not admit complete separation of the variables).

UR - http://www.scopus.com/inward/record.url?scp=21344451868&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344451868&partnerID=8YFLogxK

U2 - 10.1007/BF02065973

DO - 10.1007/BF02065973

M3 - Article

VL - 104

SP - 921

EP - 934

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

IS - 2

ER -