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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- 10.48550/arXiv.2301.03547
- arXiv:
- arXiv:2301.03547
- Bibcode:
- 2023arXiv230103547S
- Keywords:
-
- Nonlinear Sciences - Pattern Formation and Solitons;
- 35Q53;
- (Primary) 35B36 (Secondary)
- E-Print:
- 9 pages, 3 figures