複素微分方程式

複素微分方程式（ふくそびぶんほうていしき、英: Complex differential equations）は、複素関数を厳密解としてもつ微分方程式の総称であり、その解析には解析接続やモノドロミー行列をはじめとした複素解析の道具が用いられる。 超幾何微分方程式 パンルヴェ方程式 ホイン函数#ホインの方程式 リッカチの微分方程式 非線形シュレディンガー方程式 複素KdV方程式 複素mKdV方程式 複素バーガース方程式 複素短パルス方程式 (英: complex short pulse equation) 複素サイン・ゴルドン方程式 (英: complex sine-Gordon equation) 複素 Ginzburg-Landau 方程式 福原満洲雄 大島利雄 岡本和夫 高野恭一 木村俊房 神保道夫 ポール・パンルヴェ en:Lazarus Fuchs ダフィット・ヒルベルト ベルンハルト・リーマン en:Alexander Its en:Mark J. Ablowitz フックス型微分方程式 コーシー＝コワレフスカヤの定理 クニーズニク・ザモロドチコフ方程式 en:Riemann–Hilbert problem en:Riemann–Hilbert correspondence [脚注の使い方] ^ a b c Ablowitz, M. J., & Fokas, A. S. (2003). Complex variables: introduction and applications. en:Cambridge University Press. ^ a b 福原満洲雄「常微分方程式 第2版」岩波全書. ^ a b c d e 常微分方程式, 朝倉書店, 高野恭一. ^ a b 木村俊房「常微分方程式II」基礎数学講座. ^ a b Iwasaki, K., Kimura, H., Shimemura, S., & Yoshida, M. (2013). From Gauss to Painlevé: a modern theory of special functions. en:Springer Science & Business Media. ^ 原岡喜重. 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