Lax pairs for BKM hierarchy
Exactly Solvable and Integrable Systems
2025-12-29 v1 Mathematical Physics
Analysis of PDEs
Differential Geometry
math.MP
Abstract
We construct Lax pairs for the recently (2023) introduced integrable PDE systems known as the BKM equations. As many known and previously studied integrable systems are special cases of the BKM systems, our construction provides Lax pairs for many integrable hierarchies, including previously studied ones such as Camassa-Holm, Dullin-Gottwald-Holm, cKdV, Ito, and Marvan-Pavlov, as well as new ones. The corresponding pair is related to a Sturm-Liouville operator on the real line whose potential depends rationally on the spectral parameter.
Keywords
Cite
@article{arxiv.2512.22064,
title = {Lax pairs for BKM hierarchy},
author = {Andrey Yu. Konyaev and Vladimir S. Matveev},
journal= {arXiv preprint arXiv:2512.22064},
year = {2025}
}
Comments
27 pages, no figures