Invariant Reduction for Partial Differential Equations. I: Conservation Laws and Systems with Two Independent Variables
Exactly Solvable and Integrable Systems
2026-03-16 v1 Mathematical Physics
math.MP
Abstract
For a system of partial differential equations that has an extended Kovalevskaya form, a reduction procedure is presented that allows one to use a local (point, contact, or higher) symmetry of a system and a symmetry-invariant conservation law to algorithmically calculate constants of motion holding for symmetry-invariant solutions. Several examples including cases of point and higher symmetry invariance are presented and discussed. An implementation of the algorithm in Maple is provided.
Keywords
Cite
@article{arxiv.2412.02965,
title = {Invariant Reduction for Partial Differential Equations. I: Conservation Laws and Systems with Two Independent Variables},
author = {Kostya Druzhkov and Alexei Cheviakov},
journal= {arXiv preprint arXiv:2412.02965},
year = {2026}
}
Comments
21 pages