English

Conservation laws and normal forms of evolution equations

Mathematical Physics 2010-04-22 v1 Analysis of PDEs math.MP Exactly Solvable and Integrable Systems

Abstract

We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws. Examples include Harry Dym equation, Korteweg-de-Vries-type equations, and Schwarzian KdV equation. It is also shown that for linear evolution equations all their conservation laws are (modulo trivial conserved vectors) at most quadratic in the dependent variable and its derivatives.

Keywords

Cite

@article{arxiv.1003.1648,
  title  = {Conservation laws and normal forms of evolution equations},
  author = {Roman O. Popovych and Artur Sergyeyev},
  journal= {arXiv preprint arXiv:1003.1648},
  year   = {2010}
}

Comments

16 pages

R2 v1 2026-06-21T14:55:05.064Z