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Approximate Noether-type symmetries and conservation laws via partial Lagrangians for PDEs with a small parameter |
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| Authors: | AG Johnpillai AH Kara FM Mahomed |
| Institution: | 1. Department of Mathematics, Eastern University, Chenkalady, Sri Lanka;2. School of Mathematics, University of the Witwatersrand, P O Wits 2050, Johannesburg, South Africa;3. Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, P O Wits 2050, Johannesburg, South Africa;4. School of Computational and Applied Mathematics, University of the Witwatersrand, P O Wits 2050, Johannesburg, South Africa |
| Abstract: | We show how one can construct approximate conservation laws of approximate Euler-type equations via approximate Noether-type symmetry operators associated with partial Lagrangians. The ideas of the procedure for a system of unperturbed partial differential equations are extended to a system of perturbed or approximate partial differential equations. These approximate Noether-type symmetry operators do not form a Lie algebra in general. The theory is applied to the perturbed linear and nonlinear (1+1) wave equations and the Maxwellian tails equation. We have also obtained new approximate conservation laws for these equations. |
| Keywords: | Conservation laws Lagrangians Noether-type symmetries |
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