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

الملخص EN

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.