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The direct method in soliton theory / Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson.
- Format:
- Book
- Author/Creator:
- Hirota, Ryōgo, 1932-2015, author.
- Series:
- Cambridge tracts in mathematics ; 155.
- Cambridge tracts in mathematics ; 155
- Standardized Title:
- Chokusetsuhō ni yoru soriton no sūri. English
- Language:
- English
- Subjects (All):
- Solitons.
- Physical Description:
- 1 online resource (xi, 200 pages) : digital, PDF file(s).
- Edition:
- 1st ed.
- Place of Publication:
- Cambridge : Cambridge University Press, 2004.
- Language Note:
- English
- Summary:
- 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.
- Contents:
- 1. Bilinearization of soliton equations
- 2. Determinants and pfaffians
- 3. Structure of soliton equations
- 4. Backlund transformations
- Afterword
- References
- Index.
- Notes:
- Title from publisher's bibliographic system (viewed on 05 Oct 2015).
- Includes bibliographical references (p. 195-197) and index.
- ISBN:
- 1-107-15013-2
- 1-280-54012-5
- 9786610540129
- 0-511-21484-7
- 0-511-21663-7
- 0-511-21126-0
- 0-511-31541-4
- 0-511-54304-2
- 0-511-21303-4
- OCLC:
- 171139024
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