On a construction of general formal solutions for equations of the first Painlevé hierarchy. I

DOI10.1016/j.aim.2012.12.011zbMath1268.34185OpenAlexW2012638393MaRDI QIDQ1941159

Takashi Aoki, Yoko Umeta, Naofumi Honda

Publication date: 11 March 2013

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2012.12.011

zbMATH Keywords

multiple-scale analysisexact WKB analysisinstanton-type solutionthe first Painlevé hierarchy

Mathematics Subject Classification ID

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

Related Items (6)

2-parameter \(\tau\)-function for the first Painlevé equation: topological recursion and direct monodromy problem via exact WKB analysis ⋮ Quantum curve and the first Painlevé equation ⋮ 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 ⋮ Lax pairs for one of hierarchies similar to the first Painlevé hierarchy ⋮ General formal solutions for a unified family of \(P_{\mathrm{J}}\)-hierarchies (J=I, II, IV, 34)

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