The direct method in soliton theory
著者
書誌事項
The direct method in soliton theory
（Cambridge tracts in mathematics, 155）
Cambridge University Press, 2004
- : hbk
- タイトル別名
-
直接法によるソリトンの数理
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注記
Includes bibliographical references (p. 195-197) and index
First published in Japanese as "Chokusetsuhō ni yoru soriton no sūri" by Iwanami Shoten in 1992
内容説明・目次
内容説明
The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory.
目次
- Preface
- Foreword
- 1. Bilinearization of soliton equations
- 2. Determinants and pfaffians
- 3. Structure of soliton equations
- 4. Backlund transformations
- Afterword
- References
- Index.
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