On perturbations retaining conservation laws of difftrential equations
Abstract
The paper deals with perturbations of the equation that have a number of conservation laws. When a small term is added to the equation its conserved quantities usually decay at individual rates, a phenomenon known as a selective decay. These rates are described by the simple law using the conservation laws' generating functions and the added term. Yet some perturbation may retain a specific quantity(s), such as energy, momentum and other physically important characteristics of solutions. We introduce a procedure for finding such perturbations and demonstrate it by examples including the KdV-Burgers equation and a system from magnetodynamics. Some interesting properties of solutions of such perturbed equations are revealed and discussed.
Keywords
Cite
@article{arxiv.2301.03547,
title = {On perturbations retaining conservation laws of difftrential equations},
author = {Alexey Samokhin},
journal= {arXiv preprint arXiv:2301.03547},
year = {2023}
}
Comments
9 pages, 3 figures