Invariant variational principles and conservation laws for some nonlinear partial differential equations with constant coefficients – I

The invariance under a one-parameter infinitesimal transformation groups [1] has been proven for a number of nonlinear partial differential equations (NLPDEs) with constant coefficients, which appear in a wide variety of modelling physical phenomena/applications. The invariance identities of Rund [2] involving the Lagrangian and the generators of the infinitesimal Lie groups are utilized, for writing down the conservation laws via Noetherʹs theorem. In order that the study becomes more exhaustive, we have applied the above technique to the cases arising from the generalized Klein–Gordon equation by transforming it to ordinary differential equation (ODE), to get on exact solution for it.