The (3+1)-dimensional dispersionless integrable hierarchy and nonlinear Riemann-Hilbert problem associated with the Doubrov-Ferapontov modified heavenly equation

2025/04/17 by Ge Yi, Bowen Sun, Yi, Ge +5
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2504.12624

openalex publication_date 2025/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

According to the classification of integrable complex Monge-Ampere equations by Doubrov and Ferapontov, the modified heavenly equation is a typical (3+1)-dimensional dispersionless and canonical integrable equation.In this paper we use the eigenfunctions of the Doubrov-Ferapontov modified heavenly equation to obtain a related hierarchy. Next we construct the Lax-Sato equations with Hamiltonian vector fields and Zakharov-Shabat type equations which are equivalent to the hierarchy. The nonlinear Riemann-Hilbert problem is also applied to study the solution of Doubrov-Ferapontov modified heavenly equation.

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