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arXiv · 2402.10317

Two-component integrable extension of general heavenly equation

Wojciech Kryński·Artur Sergyeyev
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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.

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Wojciech Kryński, Artur Sergyeyev. 2024-02-15. Two-component integrable extension of general heavenly equation. https://arxiv.org/abs/2402.10317

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