English

Simplest potential conservation laws of linear evolution equations

Mathematical Physics 2011-11-28 v2 Analysis of PDEs math.MP Exactly Solvable and Integrable Systems

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

R2 v1 2026-06-21T16:06:16.487Z