Classification of the Lie and Noether point symmetries for the Wave and the Klein–Gordon equations in pp-wave spacetimes

•A complete classification of the Lie and Noether point symmetries for the Klein–Gordon and for the wave equation in pp-wave spacetimes is obtained.•The classification analysis is carried out by reducing the problem of the determination of the point symmetries to the problem of existence of conforma...

Full description

Saved in:
Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2018-02, Vol.55, p.68-83
Main Authors: Paliathanasis, A., Tsamparlis, M., Mustafa, M.T.
Format: Article
Language:English
Subjects:
Classification
Collineations
Klein-Gordon equation
Lie groups
Lie point symmetries
Mathematical analysis
pp-waves spacetimes
Schrodinger equation
Spacetime
Symmetry
Vectors (mathematics)
Wave equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•A complete classification of the Lie and Noether point symmetries for the Klein–Gordon and for the wave equation in pp-wave spacetimes is obtained.•The classification analysis is carried out by reducing the problem of the determination of the point symmetries to the problem of existence of conformal killing vectors on the pp-wave spacetimes.•The functional form of the potential is determined in which the Klein–Gordon equation admits point symmetries and Noetherian conservation law. Further the point and Noether symmetries of the wave equation are derived. A complete classification of the Lie and Noether point symmetries for the Klein–Gordon and the wave equation in pp-wave spacetimes is obtained. The classification analysis is carried out by reducing the problem of the determination of the point symmetries to the problem of existence of conformal killing vectors on the pp-wave spacetimes. Employing the existing results for the isometry classes of the pp-wave spacetimes, the functional form of the potential is determined for which the Klein–Gordon equation admits point symmetries and Noetherian conservation law. Finally the Lie and Noether point symmetries of the wave equation are derived.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2017.06.001