English

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}
}