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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2503.00889 |
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| _version_ | 1866916639041126400 |
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| author | Xu, Xiaoxue Yi, Decong Li, Xing Zhang, Da-jun |
| author_facet | Xu, Xiaoxue Yi, Decong Li, Xing Zhang, Da-jun |
| contents | Algebro-geometric solutions for the discrete Chen-Lee-Liu (CLL) system are derived in this paper. We construct a nonlinear integrable symplectic map which is used to define discrete phase flows. Compatibility of the maps with different parameters gives rise to the discrete CLL system whose solutions (discrete potentials) can be formulated through the discrete phase flows. Baker-Akhiezer functions are introduced and their asymptotic behaviors are analyzed. Consequently, we are able to reconstruct the discrete potentials in terms of the Riemann theta functions. These results can be extended to 3-dimensional case and algebro-geometric solutions of the discrete modified Kadomtsev-Petviashvili equation are obtained. Some solutions of genus one case are illustrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebro-geometric integration to the discrete Chen-Lee-Liu system Xu, Xiaoxue Yi, Decong Li, Xing Zhang, Da-jun Exactly Solvable and Integrable Systems 35Q51, 37K60, 39A36 Algebro-geometric solutions for the discrete Chen-Lee-Liu (CLL) system are derived in this paper. We construct a nonlinear integrable symplectic map which is used to define discrete phase flows. Compatibility of the maps with different parameters gives rise to the discrete CLL system whose solutions (discrete potentials) can be formulated through the discrete phase flows. Baker-Akhiezer functions are introduced and their asymptotic behaviors are analyzed. Consequently, we are able to reconstruct the discrete potentials in terms of the Riemann theta functions. These results can be extended to 3-dimensional case and algebro-geometric solutions of the discrete modified Kadomtsev-Petviashvili equation are obtained. Some solutions of genus one case are illustrated. |
| title | Algebro-geometric integration to the discrete Chen-Lee-Liu system |
| topic | Exactly Solvable and Integrable Systems 35Q51, 37K60, 39A36 |
| url | https://arxiv.org/abs/2503.00889 |