The exact steepest descent method — a new steepest descent method based on the exact WKB analysis

Aoki, Takashi; Kawai, Takahiro; Takei, Yoshitsugu

doi:10.2969/aspm/04210045

VOL. 42 | 2004 The exact steepest descent method — a new steepest descent method based on the exact WKB analysis

Chapter Author(s) Takashi Aoki, Takahiro Kawai, Yoshitsugu Takei

Editor(s) Kimio Miyajima, Mikio Furushima, Hideaki Kazama, Akio Kodama, Junjiro Noguchi, Takeo Ohsawa, Hajime Tsuji, Tetsuo Ueda

Adv. Stud. Pure Math., 2004: 45-61 (2004) DOI: 10.2969/aspm/04210045

Abstract

Introducing a new notion of the exact steepest descent path, we develop a new steepest descent method applicable to general ordinary differential equations with polynomial coefficients. Its application to the connection problem for solutions is also discussed.