Virtual turning points — A gift of microlocal analysis to the exact WKB analysis

Takashi Aoki, Naofumi Honda, Takahiro Kawai, Tatsuya Koike, Yukihiro Nishikawa, Shunsuke Sasaki, Akira Shudo and Yoshitsugu Takei
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Takashi Aoki: Kinki University, School of Science and Engineering
Naofumi Honda: Hokkaido University, Department of Mathematics, Graduate School of Science
Takahiro Kawai: Kyoto University, Research Institute for Mathematical Sciences
Tatsuya Koike: Kyoto University, Department of Mathematics, Graduate School of Science
Yukihiro Nishikawa: Hitachi Ltd.
Shunsuke Sasaki: Mitsubishi UFJ Securities Co. Ltd.
Akira Shudo: Tokyo Metropolitan University, Department of Physics, Graduate School of Science
Yoshitsugu Takei: Kyoto University, Research Institute for Mathematical Sciences

A chapter in Algebraic Analysis of Differential Equations, 2008, pp 29-43 from Springer

Abstract: Abstract Several aspects of the notion of virtual turning points are discussed; its background, its relevance to the bifurcation phenomena of a Stokes curve, its importance in the analysis of the Noumi-Yamada system (a particular higher order Painlevé equation) and a concrete recipe for locating them. Examples given here make it manifest that virtual turning points are indispensable in WKB analysis of higher order linear ordinary differential equations with a large parameter.

Keywords: Turning Point; Microlocal Analysis; Instanton Expansion; Stokes Phenomenon; High Order Linear (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-73240-2_5

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DOI: 10.1007/978-4-431-73240-2_5

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