A unified approach to the AKNS, DNLS, KP and mKP hierarchies in the anti-self-dual Yang-Mills reduction
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914417446223872 |
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| author | Li, Shangshuai Maruno, Ken-ichi Zhang, Da-jun |
| author_facet | Li, Shangshuai Maruno, Ken-ichi Zhang, Da-jun |
| contents | We show a unified approach to the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and the unreduced derivative nonlinear Schrödinger (DNLS) hierarchies (including the Kaup-Newell, Chen-Lee-Liu, Gerdjikov-Ivanov and a generalized DNLS), together with their multi-component extensions, in the framework of the anti-self-dual Yang-Mills (ASDYM) reduction. By restricting the gauge group to GL(2), the Kadomtsev-Petviashvili (KP) and modified KP (mKP) hierarchies are formulated in the ASDYM reduction via squared eigenfunction symmetry constraints. In this case, the bilinearization of the generalized DNLS equations can also be understood through this reduction. Finally, Gram-type exact solutions for the relevant equations are presented in terms of quasi-determinants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23060 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A unified approach to the AKNS, DNLS, KP and mKP hierarchies in the anti-self-dual Yang-Mills reduction Li, Shangshuai Maruno, Ken-ichi Zhang, Da-jun Exactly Solvable and Integrable Systems We show a unified approach to the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and the unreduced derivative nonlinear Schrödinger (DNLS) hierarchies (including the Kaup-Newell, Chen-Lee-Liu, Gerdjikov-Ivanov and a generalized DNLS), together with their multi-component extensions, in the framework of the anti-self-dual Yang-Mills (ASDYM) reduction. By restricting the gauge group to GL(2), the Kadomtsev-Petviashvili (KP) and modified KP (mKP) hierarchies are formulated in the ASDYM reduction via squared eigenfunction symmetry constraints. In this case, the bilinearization of the generalized DNLS equations can also be understood through this reduction. Finally, Gram-type exact solutions for the relevant equations are presented in terms of quasi-determinants. |
| title | A unified approach to the AKNS, DNLS, KP and mKP hierarchies in the anti-self-dual Yang-Mills reduction |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2603.23060 |