Equivalent Lagrangians are used to find, via transformations, solutions and conservation laws of a given differential equation by exploiting the possible existence of an isomorphic algebra of Lie point symmetries and, more particularly, an isomorphic Noether point symmetry algebra. Applications include ordinary differential equations such as the Kummer equation and the combined gravity-inertial-Rossbywave equation and certain classes of partial differential equations related to multidimensional wave equations.
"Equivalent Lagrangians: Generalization, Transformation Maps, and Applications." J. Appl. Math. 2012 (SI14) 1 - 19, 2012. https://doi.org/10.1155/2012/860482