WKB analysis of higher order Painlevé equations with a large parameter. II. Structure theorem for instanton-type solutions of \((P_J)_m (J= I, 34\), II-2 or IV) near a simple \(P\)-turning point of the first kind

DOI10.2977/PRIMS/34zbMath1228.34144OpenAlexW1977951831MaRDI QIDQ533371

Yoshitsugu Takei, Takahiro Kawai

Publication date: 3 May 2011

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/34

zbMATH Keywords

exact WKB analysisinstanton-type solutionsPainlevé hierarchy\(P\)-turning pointshigher order Painlevé equations

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (3)

On the Stokes geometry of a unified family of \(P_{\mathrm{J}}\)-hierarchies (J=I, II, IV, 34) ⋮ Instanton-type solutions for the second and the fourth Painlevé hierarchies with a large parameter ⋮ General formal solutions for a unified family of \(P_{\mathrm{J}}\)-hierarchies (J=I, II, IV, 34)

Cites Work

• WKB analysis of Painlevé transcendents with a large parameter. III: Local reduction of 2-parameter Painlevé transcendents
• On a generalized \(2+1\) dispersive water wave hierarchy
• WKB analysis of Painlevé transcendents with a large parameter. I
• WKB analysis of higher order Painlevé equations with a large parameter -- local reduction of 0-parameter solutions for Painlevé hierarchies \((P_{J})\) (\(J=\text{ I, II-1 or II-2}\))
• Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems
• Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach
• ON THE HOLONOMIC DEFORMATION OF LINEAR DIFFERENTIAL EQUATIONS WITH A REGULAR SINGULAR POINT AND AN IRREGULAR SINGULAR POINT
• Nonisospectral scattering problems: A key to integrable hierarchies
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