Wave functions and k-point functions for the AKNS hierarchy
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918307490168832 |
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| author | Fu, Ang |
| author_facet | Fu, Ang |
| contents | For an arbitrary solution to the AKNS hierarchy, the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method [14,21]. In this paper, we introduce a pair of wave functions of the solution and we use them to express the corresponding matrix resolvent. Based on this, we derive a new formula for the k-point correlation function of the AKNS hierarchy expressed in terms of wave functions. As an application, we show that the tau-function of an arbitrary solution to the AKNS hierarchy is a KP tau-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18211 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wave functions and k-point functions for the AKNS hierarchy Fu, Ang Mathematical Physics Exactly Solvable and Integrable Systems For an arbitrary solution to the AKNS hierarchy, the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method [14,21]. In this paper, we introduce a pair of wave functions of the solution and we use them to express the corresponding matrix resolvent. Based on this, we derive a new formula for the k-point correlation function of the AKNS hierarchy expressed in terms of wave functions. As an application, we show that the tau-function of an arbitrary solution to the AKNS hierarchy is a KP tau-function. |
| title | Wave functions and k-point functions for the AKNS hierarchy |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2601.18211 |