Open Access
July, 2019 General formal solutions for a unified family of $P_{\mathrm{J}}$-hierarchies (J=I, II, IV, 34)
J. Math. Soc. Japan 71(3): 979-1003 (July, 2019). DOI: 10.2969/jmsj/78567856


A unified family of $P_{\mathrm{J}}$-hierarchies (J=I, II, IV, 34) with a large parameter is introduced and we construct general formal solutions which are called instanton-type solutions for the system.

Funding Statement

This work was supported by JSPS KAKENHI Grant No.15K17557.


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Yoko UMETA. "General formal solutions for a unified family of $P_{\mathrm{J}}$-hierarchies (J=I, II, IV, 34)." J. Math. Soc. Japan 71 (3) 979 - 1003, July, 2019.


Received: 4 August 2017; Revised: 28 March 2018; Published: July, 2019
First available in Project Euclid: 24 April 2019

zbMATH: 07121560
MathSciNet: MR3984249
Digital Object Identifier: 10.2969/jmsj/78567856

Primary: 34E20
Secondary: 34M25 , 34M55

Keywords: instanton-type solutions , Painlevé hierarchy , the exact WKB analysis

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 3 • July, 2019
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