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Conserved Forms derived from Symmetries
Author(s) -
Muriel C.,
Romero J.L.
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810747
Subject(s) - homogeneous space , symmetry (geometry) , ordinary differential equation , scalar (mathematics) , point (geometry) , mathematics , computation , spacetime symmetries , order (exchange) , mathematical physics , differential equation , pure mathematics , algebra over a field , physics , mathematical analysis , quantum mechanics , algorithm , geometry , quantum field theory in curved spacetime , finance , economics , quantum , quantum gravity
For first order scalar ordinary differential equations, a well–known result of Sophus Lie states that a Lie point symmetry can be used to construct an integrating factor and conversely. However, there exist higher order equations without Lie point symmetries that admit integrating factors or that are exact. We present a method based on λ‐symmetries to calculate integrating factors. An example of a second order equation without Lie point symmetries illustrates how the method works in practice and how the computations that appear in other methods may be simplified. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)