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

Abstract

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.

17 pages, no figures

References in corpus (5)

• Two dimensional dynamical systems which admit Lie and Noether symmetries
• Lie point symmetries of a general class of PDEs: The heat equation
• Symmetry analysis of the Klein-Gordon equation in Bianchi I spacetimes
• Lie and Noether point symmetries of a class of quasilinear systems of second-order differential equations
• Applications of Symmetry Methods to the Theory of Plasma Physics

Cited by in corpus (3)

• Lie symmetries and similarity solutions for rotating shallow water
• Quadratic integrals of a multi-scalar cosmological model
• Lie symmetry analysis and similarity solutions for the Camassa-Choi equations