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Variational Formulation of Approximate Symmetries and Conservation Laws

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Abstract

We show how the conserved vectors and associated (approximate) Lie symmetry generators of a partial differential equation with a small parameter can be utilized to construct approximate Lagrangians for the equation. We then use the Lagrangian to further determine approximate Noether symmetries and, hence, new associated conservation laws. The theory is applied to a number of perturbations of the wave equation.

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Authors and Affiliations

  1. Department of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Johannesburg, South Africa

    A. G. Johnpillai & A. H. Kara

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  1. A. G. Johnpillai
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  2. A. H. Kara
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Correspondence to A. H. Kara.

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Johnpillai, A.G., Kara, A.H. Variational Formulation of Approximate Symmetries and Conservation Laws. International Journal of Theoretical Physics 40, 1501–1509 (2001). https://doi.org/10.1023/A:1017561629174

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  • DOI: https://doi.org/10.1023/A:1017561629174

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