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arXiv · 1810.09556

On the relationship between the invariance and conservation laws of differential equations

A H Kara
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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.

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A H Kara. 2018-10-09. On the relationship between the invariance and conservation laws of differential equations. https://arxiv.org/abs/1810.09556

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