A Basis of Conservation Laws for Partial Differential Equations

SUMMARYAfter the initial seminal works of Sophus Lie on ordinary differential equations, several important results on point symmetry group analysis of ordinary differential equations have been obtained. In this review, we present the salient features of point symmetry group classification of scalar ordinary differential equations: linear nth-order, second-order equations as well as related results. The main focus here is the contributions of Peter Leach, in this area, in whose honour this paper is written on the occasion of his 65th birthday celebrations.

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“…It is known that a symmetry algebra of a first integral is a subalgebra of the underlying equation that gave rise to the first integral [38].…”

Section: Symmetries Associated With First Integralsmentioning

confidence: 99%

“…[28,[33][34][35][36][37][38][39] Suppose that J is a first integral of a scalar nth-order ordinary differential equation…”

Section: Examplementioning

confidence: 99%

Symmetry group classification of ordinary differential equations: Survey of some results

Mahomed

2007

Math Methods in App Sciences

111

110

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“…Similarly, since X 1 (Q 4 ) = −aQ 2 , the action of X 1 on Q 4 yields Q 2 so that Q 2 as an independent multiplier can be dispensed with. That is, the conserved vector from Q 2 would not be in the basis set of conservation laws (see [8]). …”

Section: Resultsmentioning

confidence: 99%

“…The use of symmetry properties of a given system of partial differential equations to construct or generate new conservation laws from known conservation laws has been investigated [7,8].…”

Section: Introductionmentioning

confidence: 99%

An Analysis of the Symmetries and Conservation Laws of the Class of Zakharov-Kuznetsov Equations

Kara

2010

MCA

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Abstract-In this paper, we study and classify the conservation laws of the ZakharovKuznetsov equations. It is shown that these can be obtained by studying the interplay between symmetry generators and 'multipliers'. This is, particularly, useful for the higher-order multipliers. As a final note, we include Drinfeld-Sokolov-Wilson system to demonstrate the usefulness of the approach to systems of pdes.

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“…The conserved vectors can be determined from Eq. (17) [26,27]. We determine conservation laws using two techniques outlined below.…”

Section: Conservation Lawsmentioning

confidence: 99%

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

Ndlovu

Moitsheki

2013

Open Physics

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Abstract:Some new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.PACS (

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A Basis of Conservation Laws for Partial Differential Equations

Cited by 111 publications

References 16 publications

Symmetry group classification of ordinary differential equations: Survey of some results

Symmetry group classification of ordinary differential equations: Survey of some results

An Analysis of the Symmetries and Conservation Laws of the Class of Zakharov-Kuznetsov Equations

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

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