Equivalent lagrangians and transformation maps for differential equations

Abstract

The Method of Equivalent Lagrangians is used to find the solutions of a given differential equation by exploiting the possible existence of an isomorphic Lie point symmetry algebra and, more particularly, an isomorphic Noether point symmetry algebra. Applications include ordinary differential equations such as the Kummer Equation and the Combined Gravity-Inertial-Rossby Wave Equation and certain classes of partial differential equations related to the (1 + 1) linear wave equation. We also make generalisations to the (2 + 1) and (3 + 1) linear wave equations.