The direct method in soliton theory
By: Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo and Claire Gilson
Series: Cambridge tracts in mathematics -- 155
Publisher: Cambridge University Press
Published: 2004
Place of publication: Cambridge, U.K; New York
Language: eng
Number of pages: 200
Subjects: Solitons
Work titles: Chokusetsuhō ni yoru soriton no sūri.
Description: 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.
Notes: Includes bibliographical references (p. 195-197) and index