Group invariant transformations for the Klein-Gordon equation in three dimensional flat spaces

JOURNAL OF GEOMETRY AND PHYSICS

卷:117

Article

Jamal, Sameerah^1,2  Paliathanasis, Andronikos^3,4 

[1] Univ Witwatersrand, Sch Math, Johannesburg, South Africa

[2] Univ Witwatersrand, Ctr Differential Equat Continuum Mech & Applicat, Johannesburg, South Africa

[3] Univ Austral Chile, Inst Ciencias Fis & Matemat, Valdivia, Chile

[4] Durban Univ Technol, Inst Syst Sci, POB 1334, ZA-4000 Durban, South Africa

关键词: Lie symmetry;    Potential functions;    Klein-Gordon equation;    Invariant solutions;   

DOI  :  10.1016/j.geomphys.2017.03.003

来源: Elsevier

【 摘 要 】

We perform the complete symmetry classification of the Klein-Gordon equation in maximal symmetric spacetimes. The central idea is to find all possible potential functions V(t, x, y) that admit Lie and Noether symmetries. This is done by using the relation between the symmetry vectors of the differential equations and the elements of the conformal algebra of the underlying geometry. For some of the potentials, we use the admitted Lie algebras to determine corresponding invariant solutions to the Klein-Gordon equation. An integral part of this analysis is the problem of the classification of Lie and Noether point symmetries of the wave equation. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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