Long-time asymptotic series for the Painleve II equation: Riemann-Hilbert approach
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916801261076480 |
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| author | Iorgov, N. Zhuravlov, Yu. |
| author_facet | Iorgov, N. Zhuravlov, Yu. |
| contents | We elaborate a systematic way to obtain higher order contributions in the nonlinear steepest descent method for Riemann-Hilbert problem associated with homogeneous Painleve II equation. The problem is reformulated as a matrix factorization problem on two circles and can be solved perturbatively reducing it to finite systems of algebraic linear equations. The method is applied to find explicitly long-time asymptotic behaviour for tau function of Painleve II equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17051 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Long-time asymptotic series for the Painleve II equation: Riemann-Hilbert approach Iorgov, N. Zhuravlov, Yu. Exactly Solvable and Integrable Systems Mathematical Physics We elaborate a systematic way to obtain higher order contributions in the nonlinear steepest descent method for Riemann-Hilbert problem associated with homogeneous Painleve II equation. The problem is reformulated as a matrix factorization problem on two circles and can be solved perturbatively reducing it to finite systems of algebraic linear equations. The method is applied to find explicitly long-time asymptotic behaviour for tau function of Painleve II equation. |
| title | Long-time asymptotic series for the Painleve II equation: Riemann-Hilbert approach |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2311.17051 |