Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlevé-type equations
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913169078747136 |
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| author | Dai, Dan Yue, Xiaolu |
| author_facet | Dai, Dan Yue, Xiaolu |
| contents | In this paper, we establishes a connection between noncommutative Laurent biorthogonal polynomials (bi-OPs) and matrix discrete Painlevé (dP) equations. We first apply nonisospectral deformations to noncommutative Laurent bi-OPs to obtain the noncommutative nonisospectral mixed relativistic Toda lattice and its Lax pair. Then, we perform a stationary reduction on this Lax pair to obtain a matrix dP-type equation. The validity of this reduction is demonstrated through a specific choice of weight function and the application of quasideterminant properties. In the scalar case, our matrix dP equation reduces to the known alternate dP II equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlevé-type equations Dai, Dan Yue, Xiaolu Exactly Solvable and Integrable Systems Mathematical Physics In this paper, we establishes a connection between noncommutative Laurent biorthogonal polynomials (bi-OPs) and matrix discrete Painlevé (dP) equations. We first apply nonisospectral deformations to noncommutative Laurent bi-OPs to obtain the noncommutative nonisospectral mixed relativistic Toda lattice and its Lax pair. Then, we perform a stationary reduction on this Lax pair to obtain a matrix dP-type equation. The validity of this reduction is demonstrated through a specific choice of weight function and the application of quasideterminant properties. In the scalar case, our matrix dP equation reduces to the known alternate dP II equation. |
| title | Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlevé-type equations |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2510.27402 |