The (3+1)-dimensional dispersionless integrable hierarchy and nonlinear Riemann-Hilbert problem associated with the Doubrov-Ferapontov modified heavenly equation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913797254414336 |
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| author | Yi, Ge Sun, Bowen Tian, Kelei Xu, Ying |
| author_facet | Yi, Ge Sun, Bowen Tian, Kelei Xu, Ying |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The (3+1)-dimensional dispersionless integrable hierarchy and nonlinear Riemann-Hilbert problem associated with the Doubrov-Ferapontov modified heavenly equation Yi, Ge Sun, Bowen Tian, Kelei Xu, Ying Exactly Solvable and Integrable Systems 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. |
| title | The (3+1)-dimensional dispersionless integrable hierarchy and nonlinear Riemann-Hilbert problem associated with the Doubrov-Ferapontov modified heavenly equation |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2504.12624 |