On the formulation of the NQC variable
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917168227024896 |
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| author | Shi, Leilei Zhang, Cheng Zhang, Da-jun |
| author_facet | Shi, Leilei Zhang, Cheng Zhang, Da-jun |
| contents | The Nijhoff-Quispel-Capel (NQC) equation is a general lattice quadrilateral equation presented in terms of a function $S(a,b)$ where $a$ and $b$ serve as extra parameters. It can be viewed as the counterpart of Q3 equation which is the second top equation in the Adler-Bobenko-Suris list. In this paper, we review some known formulations of the NQC variable $S(a,b)$, such as the Cauchy matrix approach, the eigenfunction approach and via a spectral Wronskian. We also present a new perspective to formulate $S(a,b)$ from the eigenfunctions of a Lax pair of the lattice (non-potential) modified Korteweg de Vries equation. A new Dbar problem is introduced and employed in the derivation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the formulation of the NQC variable Shi, Leilei Zhang, Cheng Zhang, Da-jun Exactly Solvable and Integrable Systems The Nijhoff-Quispel-Capel (NQC) equation is a general lattice quadrilateral equation presented in terms of a function $S(a,b)$ where $a$ and $b$ serve as extra parameters. It can be viewed as the counterpart of Q3 equation which is the second top equation in the Adler-Bobenko-Suris list. In this paper, we review some known formulations of the NQC variable $S(a,b)$, such as the Cauchy matrix approach, the eigenfunction approach and via a spectral Wronskian. We also present a new perspective to formulate $S(a,b)$ from the eigenfunctions of a Lax pair of the lattice (non-potential) modified Korteweg de Vries equation. A new Dbar problem is introduced and employed in the derivation. |
| title | On the formulation of the NQC variable |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2510.26327 |