Symmetries, conservation laws, and wave equation on the Milne metric. (English) Zbl 1267.35018

Ahmad, Ahmad M.; Bokhari, Ashfaque H.; Zaman, F. D.

J. Appl. Math. 2012, Article ID 153817, 7 p. (2012).

Summary: Noether symmetries provide conservation laws that are admitted by Lagrangians representing physical systems. For partial differential equation possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. In this paper we provide a systematic procedure for determining Noether symmetries and conserved vectors for a Lagrangian constructed from a Lorentzian metric of interest in mathematical physics. For completeness, we give Lie point symmetries and conservation laws admitted by the wave equation on this Lorentzian metric.

MSC:

35B06	Symmetries, invariants, etc. in context of PDEs
35L05	Wave equation

Keywords:

Noether symmetries; conserved vectors; Lie point symmetries

References:

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