Approximate Noether-type symmetries and conservation laws via partial Lagrangians for PDEs with a small parameter
✍ Scribed by A.G. Johnpillai; A.H. Kara; F.M. Mahomed
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 594 KB
- Volume
- 223
- Category
- Article
- ISSN
- 0377-0427
No coin nor oath required. For personal study only.
✦ Synopsis
We show how one can construct approximate conservation laws of approximate Euler-type equations via approximate Noethertype 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.