On the Relationship between the Invariance and Conservation Laws of Differential Equations

A. H. Kara

Journal of Mathematics, 2018, vol. 2018, 1-5

Abstract:

In this paper, we highlight the complimentary nature of the results of Anco & Bluman and Ibragimov in the construction of conservation laws that whilst the former establishes the role of multipliers, the latter presents a formal procedure to determine the flows. Secondly, we show that there is an underlying relationship between the symmetries and conservation laws in a general setting, extending the results of Kara & Mahomed. The results take apparently differently forms for point symmetry generators and higher-order symmetries. Similarities exist, to some extent, with a previously established result relating symmetries and multipliers of a differential equation. A number of examples are presented.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2952583

DOI: 10.1155/2018/2952583

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