Abstract
The method of noncommutative integration of linear differential equations [A. V. Shapovalov and I. V. Shirokov, Izv. Vyssh. Uchebn. Zaved. Fiz., No. 4, 116; No. 5, 100 (1991)] is used to integrate the Klein-Gordon equation in Riemannian spaces. The situation is investigated where the set of noncommuting symmetry operators of the Klein-Gordon equation consists of first-order operators and one second-order operator and forms a so-called F algebra, which generalizes the concept of a Lie algebra. The F algebra is a quadratic algebra in the given situation. A classification of four- and five-dimensional F algebras is given. The integration of the Klein-Gordon equation in a Riemannian space, which does not admit separation of variables, is demonstrated in a nontrivial example.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
