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The Direct Method in Soliton Theory - Hirota, Ryogo, and Nagai, Atsushi (Edited and translated by), and Nimmo, Jon (Edited and translated by)
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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 ...

The Direct Method in Soliton Theory 2004, Cambridge University Press, Cambridge

ISBN-13: 9780521836609