Multivariable Painleve'-II equation: connection formulas for asymptotic solutions
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912984813535232 |
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| author | Sinitsyn, N. A. |
| author_facet | Sinitsyn, N. A. |
| contents | It is shown that a generalization of the Painlevé-II equation (P-II) to a system of coupled equations with symmetry breaking terms is integrable. A Lax pair for this system is used to relate the asymptotic behavior of the solutions at different infinities via an asymptotically exact WKB approach. The analysis relies on an exact solution of the quantum mechanical Demkov-Osherov model (DOM). An application to the problem of unstable vacuum decay during a second order phase transition provides precise scaling of the number of excitations, including subdominant contributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22470 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multivariable Painleve'-II equation: connection formulas for asymptotic solutions Sinitsyn, N. A. Mathematical Physics General Relativity and Quantum Cosmology Exactly Solvable and Integrable Systems Quantum Physics It is shown that a generalization of the Painlevé-II equation (P-II) to a system of coupled equations with symmetry breaking terms is integrable. A Lax pair for this system is used to relate the asymptotic behavior of the solutions at different infinities via an asymptotically exact WKB approach. The analysis relies on an exact solution of the quantum mechanical Demkov-Osherov model (DOM). An application to the problem of unstable vacuum decay during a second order phase transition provides precise scaling of the number of excitations, including subdominant contributions. |
| title | Multivariable Painleve'-II equation: connection formulas for asymptotic solutions |
| topic | Mathematical Physics General Relativity and Quantum Cosmology Exactly Solvable and Integrable Systems Quantum Physics |
| url | https://arxiv.org/abs/2603.22470 |