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Cambridge Tracts in Mathematics : The Direct Method in Soliton Theory Series Number 155 - Ryogo Hirota

Cambridge Tracts in Mathematics

The Direct Method in Soliton Theory Series Number 155

By: Ryogo Hirota, Atsushi Nagai (Editor), Jon Nimmo (Editor), Claire Gilson (Editor)

Hardcover Published: 16th August 2004
ISBN: 9780521836609
Number Of Pages: 214

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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.

'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 ' ... a nice example of a mathematical writing that can be read at nearly normal pace, which is extremely rare nowadays.' Zentralblatt MATH

Bilinearization of soliton equations
Determinants and pfaffians
Structure of soliton equations
Backlund transformations
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521836609
ISBN-10: 0521836603
Series: Cambridge Tracts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 214
Published: 16th August 2004
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.9 x 15.2  x 1.3
Weight (kg): 0.46