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Partial Noether operators and first integrals via partial Lagrangians

✍ Scribed by A. H. Kara; F. M. Mahomed; I. Naeem; C. Wafo Soh

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
119 KB
Volume
30
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The notions of partial Lagrangians, partial Noether operators and partial Euler–Lagrange equations are used in the construction of first integrals for ordinary differential equations that need not be derivable from variational principles. We obtain a Noether‐like theorem that provides the first integral by means of a formula which has the same structure as the Noether integral. However, the invariance
condition for the determination of the partial Noether operators is different as we have a partial Lagrangian and as a result partial Euler–Lagrange equations. Applications given include those that admit a standard Lagrangian such as the harmonic oscillator, modified Emden and Ermakov–Pinney equations and systems of two second‐order equations that do not have standard Lagrangians. Copyright Β© 2007 John Wiley & Sons, Ltd.

πŸ“œ SIMILAR VOLUMES

Approximate Noether-type symmetries and
Approximate Noether-type symmetries and conservation laws via partial Lagrangians for PDEs with a small parameter
✍ A.G. Johnpillai; A.H. Kara; F.M. Mahomed πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 594 KB

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 pertur