Rigorous analytical approximation of tritronquée solution to Painlevé-I and the first singularity

DOI10.1016/j.jde.2016.06.009zbMath1352.34114arXiv1412.3782OpenAlexW2963169744MaRDI QIDQ305407

F. Blanchet-Sadri, M. Dambrine

Publication date: 29 August 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.3782

zbMATH Keywords

Painlevé \(I\) equationtritronquee solution

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

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Cites Work

• A computational exploration of the second Painlevé equation
• A numerical methodology for the Painlevé equations
• Proof of the Dubrovin conjecture and analysis of the tritronquée solutions of PI
• A direct method to find Stokes multipliers in closed form for P$_1$ and more general integrable systems
• On the spectral properties ofL_±in three dimensions
• Singularities in water waves and Rayleigh–Taylor instability
• Numerical studies of the fourth Painlevé equation
• On Boutroux's Tritronquée Solutions of the First Painlevé Equation
• Analytical Approximation of the Blasius Similarity Solution with Rigorous Error Bounds

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