Toward the exact WKB analysis of differential equations, linear or non-linear
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Bibliographic Information
Toward the exact WKB analysis of differential equations, linear or non-linear
Kyoto University Press, c2000
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Outgrowth of the symposium entitled "Algebraic Analysis of Singular Perturbations" (Nov. 30-Dec. 5, 1998, Kyoto Univ.)
Includes bibliographical references and index
Description and Table of Contents
Table of Contents
- １ Ｅｘａｃｔ ＷＫＢ ａｎａｌｙｓｉｓ ｏｆ ｌｉｎｅａｒ ｄｉｆｆｅｒｅｎｔｉａｌ ｅｑｕａｔｉｏｎｓ（Ｏｎ ａ ｃｏｍｐｌｅｔｅ ｄｅｓｃｒｉｐｔｉｏｎ ｏｆ ｔｈｅ Ｓｔｏｋｅｓ ｇｅｏｍｅｔｒｙ ｆｏｒ ｈｉｇｈｅｒ ｏｒｄｅｒ ｏｒｄｉｎａｒｙ ｄｉｆｆｅｒｅｎｔｉａｌ ｅｑｕａｔｉｏｎｓ ｗｉｔｈ ａ ｌａｒｇｅ ｐａｒａｍｅｔｅｒ ｖｉａ ｉｎｔｅｇｒａｌ ｒｅｐｒｅｓｅｎｔａｔｉｏｎｓ；Ｅｘａｃｔ ＷＫＢ ａｎａｌｙｓｉｓ ａｎｄ ｔｈｅ Ｌａｎｇｅｒ ｍｏｄｉｆｉｃａｔｉｏｎ ｗｉｔｈ ａｐｐｌｉｃａｔｉｏｎ ｔｏ ｂａｒｒｉｅｒ ｔｏｐ ｒｅｓｏｎａｎｃｅｓ ほか）
- ２ Ｈｙｐｅｒａｓｙｍｐｔｏｔｉｃｓ ａｎｄ ａｓｙｍｐｔｏｔｉｃｓ ｂｅｙｏｎｄ ａｌｌ ｏｒｄｅｒｓ（Ｃｏｎｎｅｃｔｉｏｎ ｆｏｒｍｕｌａ，ｈｙｐｅｒａｓｙｍｐｔｏｔｉｃｓ，ａｎｄ Ｓｃｈｒ¨ｏｄｉｎｇｅｒ ｅｉｇｅｎｖａｌｕｅｓ：ｄｉｓｐｅｒｓｉｖｅ ｈｙｐｅｒａｓｙｍｐｔｏｔｉｃｓ ａｎｄ ｔｈｅ ａｎｈａｒｍｏｎｉｃ ｏｓｃｉｌｌａｔｏｒ；Ａｓｙｍｐｔｏｔｉｃ ｓｔｒｕｃｔｕｒｅ ｏｆ ｍｏｖａｂｌｅ ｓｉｎｇｕｌａｒｉｔｉｅｓ ｏｆ ｓｏｌｕｔｉｏｎｓ ｏｆ ｎｏｎｌｉｎｅａｒ ａｎａｌｙｔｉｃ ｄｉｆｆｅｒｅｎｔｉａｌ ｓｙｓｔｅｍｓ ほか）
- ３ Ａｓｙｍｐｔｏｔｉｃ ａｎａｌｙｓｉｓ ａｎｄ ｓｔｒｕｃｔｕｒｅ ｏｆ ｎｏｎ‐ｌｉｎｅａｒ ｄｉｆｆｅｒｅｎｔｉａｌ ｅｑｕａｔｉｏｎｓ（Ｃａｎ ｗｅ ｆｉｎｄ ａ ｎｅｗ ｄｅｆｏｒｍａｔｉｏｎ ｏｆ （ＳＬＪ） ｗｉｔｈ ｒｅｓｐｅｃｔ ｔｏ ｔｈｅ ｐａｒａｍｅｔｅｒｓ ｃｏｎｔａｉｎｅｄ ｉｎ （ＰＪ）？；Ｔｈｅ ｉｒｒｅｄｕｃｉｂｉｌｉｔｙ ｏｆ ｔｈｅ ｓｅｃｏｎｄ Ｐａｉｎｌｅｖ´ｅ ｅｑｕａｔｉｏｎ ａｎｄ ｔｈｅ ｉｓｏｍｏｎｏｄｒｏｍｙ ｍｅｔｈｏｄ ほか）
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