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Journal of Applied Mathematics
Volume 2012, Article ID 860482, 19 pages
Research Article

Equivalent Lagrangians: Generalization, Transformation Maps, and Applications

School of Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa

Received 1 August 2012; Revised 12 September 2012; Accepted 15 September 2012

Academic Editor: Mehmet Pakdemirli

Copyright © 2012 N. Wilson and A. H. Kara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.