nth-Order Approximate Lagrangians Induced by Perturbative Geometries

  • Sameerah JamalEmail author


A family of perturbative Lagrangians that describe approximate and multidimensional Klein-Gordon equations are studied. We probe the existence of approximate Noether symmetries via generalized geometric conditions for a perturbation of any order. The knowledge of the geometric conditions uncovers that unlike exact symmetries, the approximate Noether symmetries of the Lagrangian which describes the motion of a particle in n-dimensional space under the action of an autonomous force, is inequivalent to the Noether symmetries admitted by the Klein-Gordon Lagrangian in general.


Approximate symmetries Noether symmetries Perturbations 

Mathematics Subject Classification (2010)

76M60 35Q75 34E10 35C20 58J37 


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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