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  3. The Direct Method in Soliton Theory
  • Cited by 2179
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2009
      July 2004
      ISBN:
      9780511543043
      9780521836609
      DOI:
      https://doi.org/10.1017/CBO9780511543043
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.46kg, 214 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Discrete Mathematics Information Theory and Coding
      Series:
      Cambridge Tracts in Mathematics (155)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Discrete Mathematics Information Theory and Coding
    Series:
    Cambridge Tracts in Mathematics (155)
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    Book 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.

    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.'

    Source: Zentralblatt MATH

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