Equivalent Lagrangians: generalization, transformation maps, and applications. (English) Zbl 1322.35001

Summary: 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-Rossby wave equation and certain classes of partial differential equations related to multidimensional wave equations.


35A30 Geometric theory, characteristics, transformations in context of PDEs
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