An Analysis of the Invariance and Conservation Laws of Some Classes of Nonlinear Ostrovsky Equations and Related Systems

doi:10.1088/0256-307X/28/1/010201

Chin. Phys. Lett.

2011, Vol. 28

Issue (1): 010201 DOI: 10.1088/0256-307X/28/1/010201

GENERAL

An Analysis of the Invariance and Conservation Laws of Some Classes of Nonlinear Ostrovsky Equations and Related Systems

K. Fakhar^1**, A. H. Kara²

¹Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia
²School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Johannesburg, P Bag 3 Wits 2050, South Africa

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K. Fakhar, A. H. Kara 2011 Chin. Phys. Lett. 28 010201

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Abstract A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties (through the Lie point symmetry generators) and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the 'multipliers' associated with the conservation laws with a stronger emphasis on the 'higher-order' ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.

Keywords: 02.30.Jr 02.20.Sv 02.40.Hw

Received: 08 June 2010 Published: 23 December 2010

PACS:	02.30.Jr	(Partial differential equations)
	02.20.Sv	(Lie algebras of Lie groups)
	02.40.Hw	(Classical differential geometry)

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https://cpl.iphy.ac.cn/10.1088/0256-307X/28/1/010201 OR https://cpl.iphy.ac.cn/Y2011/V28/I1/010201

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[6] Kara A H and Mahomed F M 2000 Int. J. Theor. Phys. 39 23

[7] Kara A H and Mahomed F M 2002 J. Nonlinear Math. Phys. 9 60

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[10] Olver P 1993 Application of Lie Groups to Differential Equations (New York: Springer)

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