Noncommutative nonisospectral Toda and Lotka-Volterra lattices, and matrix discrete Painlevé equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916327525974016 |
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| author | Yan, Anhui Li, Chunxia |
| author_facet | Yan, Anhui Li, Chunxia |
| contents | The noncommutative analogues of the nonisospectral Toda and Lotka-Volterra lattices are proposed and studied by performing nonisopectral deformations on the matrix orthogonal polynomials and matrix symmetric orthogonal polynomials without specific weight functions, respectively. Under stationary reductions, matrix discrete Painlevé I and matrix asymmetric discrete Painlevé I equations are derived separately not only from the noncommutative nonisospectral lattices themselves, but also from their Lax pairs. The rationality of the stationary reduction has been justified in the sense that quasideterminant solutions are provided for the corresponding matrix discrete Painlevé equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08486 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noncommutative nonisospectral Toda and Lotka-Volterra lattices, and matrix discrete Painlevé equations Yan, Anhui Li, Chunxia Exactly Solvable and Integrable Systems The noncommutative analogues of the nonisospectral Toda and Lotka-Volterra lattices are proposed and studied by performing nonisopectral deformations on the matrix orthogonal polynomials and matrix symmetric orthogonal polynomials without specific weight functions, respectively. Under stationary reductions, matrix discrete Painlevé I and matrix asymmetric discrete Painlevé I equations are derived separately not only from the noncommutative nonisospectral lattices themselves, but also from their Lax pairs. The rationality of the stationary reduction has been justified in the sense that quasideterminant solutions are provided for the corresponding matrix discrete Painlevé equations. |
| title | Noncommutative nonisospectral Toda and Lotka-Volterra lattices, and matrix discrete Painlevé equations |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2407.08486 |