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Partial Euler operators and the efficient inversion of Div

Hydon, Peter E. (2023) Partial Euler operators and the efficient inversion of Div. European Journal of Applied Mathematics, 34 (5). pp. 1046-1066. ISSN 0956-7925. (doi:10.1017/S0956792523000037) (KAR id:99905)


The problem of inverting the total divergence operator is central to finding components of a given conservation law. This might not be taxing for a low-order conservation law of a scalar partial differential equation, but integrable systems have conservation laws of arbitrarily high order that must be found with the aid of computer algebra. Even low-order conservation laws of complex systems can be hard to find and invert. This paper describes a new, efficient approach to the inversion problem. Two main tools are developed: partial Euler operators and partial scalings. These lead to a line integral formula for the inversion of a total derivative and a procedure for inverting a given total divergence concisely.

Item Type: Article
DOI/Identification number: 10.1017/S0956792523000037
Uncontrolled keywords: Conservation laws, inversion method, partial Euler operators
Subjects: Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: University of Kent (
Depositing User: Peter Hydon
Date Deposited: 05 Feb 2023 12:13 UTC
Last Modified: 18 Sep 2023 14:30 UTC
Resource URI: (The current URI for this page, for reference purposes)

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