A direct method to find Stokes multipliers in closed form for \(\mathrm{P}_1\) and more general integrable systems (Q2821663)
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scientific article; zbMATH DE number 6629237
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A direct method to find Stokes multipliers in closed form for \(\mathrm{P}_1\) and more general integrable systems |
scientific article; zbMATH DE number 6629237 |
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22 September 2016
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Stokes multiplier
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Painlevé-Kowalevski property
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asymptotically conserved quantity
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Borel summability
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Painlevé equation
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tronquées solution
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tritronquées solution
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A direct method to find Stokes multipliers in closed form for \(\mathrm{P}_1\) and more general integrable systems (English)
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In this paper, the authors introduce a new rigorous method, based on Borel summability and asymptotic constants of motion generalizing previous results, to analyze singular behavior of nonlinear ordinary differential equations of second order in a neighborhood of infinity and provide global information about their solutions in \(\mathbb{C}\). The new method allows us to calculate the Stokes multiplier without using linearization techniques such as Riemann-Hilbert or isomonodromic reformulations. The analysis is carried out in detail for the first Painlevé equation \(P_I\).
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