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The direct method in soliton theory by Atsushi Nagai, Claire Gilson, Jon Nimmo, Ryogo Hirota

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The direct method in soliton theory Atsushi Nagai, Claire Gilson, Jon Nimmo, Ryogo Hirota
Language: English
Page: 213
Format: pdf
ISBN: 0521836603, 9780521836609
Publisher: Cambridge University Press

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.