Invariance analysis and conservation laws of the wave equation on Vaidya manifolds

Pramana

A H Kara1¹  R Narain¹ 

[1] School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa$$

关键词: Wave equations on nonflat manifolds;    symmetry analysis;    conservation laws.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper we discuss symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. We show how the wave equation is altered by the underlying geometry. In particular, a range of consequences on the form of the wave equation, the symmetries and number of conservation laws, inter alia, are altered by the manifold on which the model wave rests. We find Lie and Noether point symmetries of the corresponding wave equations and give some reductions. Some interesting physical conclusions relating to conservation laws such as energy, linear and angular momenta are also determined. We also present some interesting comparisons with the standard wave equations on a flat geometry. Finally, we pursue the existence of higher-order variational symmetries of equations on nonflat manifolds.

【 授权许可】

Unknown