Simplest potential conservation laws of linear evolution equations
Abstract
Every simplest potential conservation law of any (1+1)-dimensional linear evolution equation of even order proves induced by a local conservation law of the same equation. This claim is true also for linear simplest potential conservation laws of (1+1)-dimensional linear evolution equations of odd order, which are related to linear potential systems. We also derive an effective criterion for checking whether a quadratic conservation law of a simplest linear potential system is a purely potential conservation law of a (1+1)-dimensional linear evolution equation of odd order.
Cite
@article{arxiv.1008.4851,
title = {Simplest potential conservation laws of linear evolution equations},
author = {Vyacheslav M. Boyko and Roman O. Popovych},
journal= {arXiv preprint arXiv:1008.4851},
year = {2011}
}
Comments
12 pages, contribution to the Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (June 6-10, 2010, Protaras, Cyprus); v2: minor corrections