Characteristics of Conservation Laws for Difference Equations
Grant, TJ and Hydon, PE (2013) Characteristics of Conservation Laws for Difference Equations Foundations of Computational Mathematics, 13 (4). pp. 667-692.
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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. © 2013 SFoCM.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||August 2013|
|Identification Number :||https://doi.org/10.1007/s10208-013-9151-2|
|Additional Information :||The original publication is available at http://www.springerlink.com|
|Depositing User :||Symplectic Elements|
|Date Deposited :||11 Sep 2013 11:14|
|Last Modified :||01 Aug 2014 01:08|
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