Fredholm determinant representation of the Painlevé II $τ$-function
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866929330433556480 |
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| author | Desiraju, Harini |
| author_facet | Desiraju, Harini |
| contents | We formulate the generic $τ$-function of the Painlevé II equation as a Fredholm determinant of an integrable (Its-Izergin-Korepin-Slavnov) operator. The $τ$-function depends on the isomonodromic time $t$ and two Stokes' parameters, and the vanishing locus of the $τ$-function, called the Malgrange divisor is determined by the zeros of the Fredholm determinant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_01142 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Fredholm determinant representation of the Painlevé II $τ$-function Desiraju, Harini Mathematical Physics Classical Analysis and ODEs Exactly Solvable and Integrable Systems We formulate the generic $τ$-function of the Painlevé II equation as a Fredholm determinant of an integrable (Its-Izergin-Korepin-Slavnov) operator. The $τ$-function depends on the isomonodromic time $t$ and two Stokes' parameters, and the vanishing locus of the $τ$-function, called the Malgrange divisor is determined by the zeros of the Fredholm determinant. |
| title | Fredholm determinant representation of the Painlevé II $τ$-function |
| topic | Mathematical Physics Classical Analysis and ODEs Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2008.01142 |