On the relationship between the invariance and conservation laws of differential equations
Analysis of PDEs
2018-10-24 v1 Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1810.09556,
title = {On the relationship between the invariance and conservation laws of differential equations},
author = {A H Kara},
journal= {arXiv preprint arXiv:1810.09556},
year = {2018}
}