The Direct Method in Soliton Theory
Part of Cambridge Tracts in Mathematics
- Author: Ryogo Hirota, Waseda University, Japan
- Editors and translators:
- Atsushi Nagai, Osaka City University, Japan
- Jon Nimmo, University of Glasgow
- Claire Gilson, University of Glasgow
- Date Published: September 2004
- availability: Available
- format: Hardback
- isbn: 9780521836609
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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.
Read more- Only introduction devoted to this method; author is the inventor
- Review articles don't adopt the modern view explained here
- Written using only relatively simple mathematics
Reviews & endorsements
'Overall, the book under review is a concise and essentially self-contained book, written by one of the leading researchers associated with the development of soliton theory … provides an interesting insight into the development of a straight forward method for obtaining exact solutions for wide classes of nonlinear equations.' Peter Clarkson, University of Kent
See more reviews' … a nice example of a mathematical writing that can be read at nearly normal pace, which is extremely rare nowadays.' Zentralblatt MATH
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×Product details
- Date Published: September 2004
- format: Hardback
- isbn: 9780521836609
- length: 214 pages
- dimensions: 229 x 152 x 13 mm
- weight: 0.46kg
- availability: Available
Table of Contents
Preface
Foreword
1. Bilinearization of soliton equations
2. Determinants and pfaffians
3. Structure of soliton equations
4. Bäcklund transformations
Afterword
References
Index.
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