Two-component integrable extension of general heavenly equation

2024/02/15 by Wojciech Kryński, Kryński, Wojciech, Artur Sergyeyev +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2402.10317

openalex publication_date 2024/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-Kähler, 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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