Multivariable Painleve'-II equation: connection formulas for asymptotic solutions

• URL: http://arxiv.org/abs/2603.22470v2
• Date: Fri, 27 Mar 2026 04:43:43 GMT
• Title: Multivariable Painleve'-II equation: connection formulas for asymptotic solutions
• Abstract summary: 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.<n>An application to the problem of unstable vacuum decay during a second order phase provides precise scaling of the number of excitations.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: 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.

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