Characteristics of Conservation Laws for Difference Equations

Grant, Timothy J., Hydon, Peter E. (2013) Characteristics of Conservation Laws for Difference Equations. Foundations of Computational Mathematics, 13 (4). pp. 667-692. ISSN 1615-3375. E-ISSN 1615-3383. (doi:10.1007/s10208-013-9151-2)

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http://dx.doi.org/10.1007/s10208-013-9151-2

Abstract

Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether's Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not derivations and do not obey the chain rule for derivatives. We show how these problems may be resolved and illustrate various uses of the characteristic. In particular, we establish the converse of Noether's Theorem for difference equations, we show (without taking a continuum limit) that the conservation laws in the infinite family generated by Rasin and Schiff are distinct, and we obtain all five-point conservation laws for the potential Lotka-Volterra equation.

Item Type: Article
DOI/Identification number: 10.1007/s10208-013-9151-2
Uncontrolled keywords: Conservation laws; Difference equations; Noether's Theorem;
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Q Science > QC Physics > QC20 Mathematical Physics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Peter Hydon
Date Deposited: 06 Jan 2016 09:39 UTC
Last Modified: 29 May 2019 16:39 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/52906 (The current URI for this page, for reference purposes)
Hydon, Peter E.: https://orcid.org/0000-0002-3732-4813
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