Two-component integrable extension of general heavenly equation
Differential Geometry
2024-02-19 v1 Exactly Solvable and Integrable Systems
Abstract
We introduce an integrable two-component extension of the general heavenly equation and prove that the solutions of this extension are in one-to-one correspondence with 4-dimensional hyper-para-Hermitian metrics. Furthermore, we demonstrate that if the metrics in question are hyper-para-K\"ahler, then our system reduces to the general heavenly equation. We also present an infinite hierarchy of nonlocal symmetries and a recursion operator for the system under study.
Cite
@article{arxiv.2402.10317,
title = {Two-component integrable extension of general heavenly equation},
author = {Wojciech Kryński and Artur Sergyeyev},
journal= {arXiv preprint arXiv:2402.10317},
year = {2024}
}