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The Direct Method in Soliton Theory Ryogo Hirota (Waseda University, Japan)

The Direct Method in Soliton Theory By Ryogo Hirota (Waseda University, Japan)

The Direct Method in Soliton Theory by Ryogo Hirota (Waseda University, Japan)


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Summary

The modern version of the bilinear, or Hirota's direct, method is described here using relatively simple mathematics. As the only account in book form of the modern form of the theory, it will be essential reading for all those working in soliton theory.

The Direct Method in Soliton Theory Summary

The Direct Method in Soliton Theory by Ryogo Hirota (Waseda University, Japan)

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.

The Direct Method in Soliton Theory Reviews

'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

About Ryogo Hirota (Waseda University, Japan)

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Table of Contents

Preface; Foreword; 1. Bilinearization of soliton equations; 2. Determinants and pfaffians; 3. Structure of soliton equations; 4. Backlund transformations; Afterword; References; Index.

Additional information

NPB9780521836609
9780521836609
0521836603
The Direct Method in Soliton Theory by Ryogo Hirota (Waseda University, Japan)
New
Hardback
Cambridge University Press
2004-07-22
214
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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