Differential equations for approximate solutions of Painlevé equations: application to the algebraic solutions of the Painlevé-III \((\mathrm{D}_7)\) equation

arXiv2308.16051MaRDI QIDQ6151680

Robert J. Buckingham, Peter D. Miller

Publication date: 12 February 2024

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2308.16051

zbMATH Keywords

algebraic solutionsWeierstraß equationisomonodromy methodPainlevé-III \((\mathrm{D}_7)\) equation

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Cites Work

• On the algebraic solutions of the Painlevé-III (\(\mathrm{D}_7\)) equation
• Large-degree asymptotics of rational Painlevé-IV solutions by the isomonodromy method
• Rational solutions of the Painlevé-III equation: large parameter asymptotics
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Large-degree asymptotics of rational Painlevé-II functions: noncritical behaviour
• Theta functions and non-linear equations
• The third Painlev  equation and associated special polynomials
• Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation: I
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