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The direct method in soliton theory

✍ Scribed by Ryogo Hirota, Atsushi Nagai, Jon Nimmo, Claire Gilson

Book ID
127428571
Publisher
Cambridge University Press
Year
2004
Tongue
English
Weight
1 MB
Series
Cambridge tracts in mathematics 155
Category
Library
City
Cambridge, UK; New York
ISBN
0521836603

No coin nor oath required. For personal study only.

✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

The Direct Method in Soliton Theory
The Direct Method in Soliton Theory
✍ Hirota R., Nagai A. (Ed), Nimmo J. (Ed) πŸ“‚ Library πŸ“… 2004 πŸ› Cambridge University Press 🌐 English βš– 2 MB

Hirota invented his bilinear or direct method in the early 1970s as a way of constructing soliton solutions without dealing with the cumbersome inverse scattering transform. His invention has since come to the Kyoto School and became connected with affine Lie algebras, but here Hirota explains the m

Variational method in soliton theory
Variational method in soliton theory
✍ C. P. Jisha; V. C. Kuriakose; K. Porsezian πŸ“‚ Article πŸ“… 2009 πŸ› Springer-Verlag 🌐 English βš– 129 KB
Hamiltonian methods in the theory of sol
Hamiltonian methods in the theory of solitons
✍ Ludvig D. Faddeev, Leon Takhtajan, A.G. Reyman πŸ“‚ Library πŸ“… 2007 πŸ› Springer 🌐 English βš– 4 MB

The main characteristic of this now classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schr?dinger equation, rather than the (more usual) KdV equation, is considered as a main example. The inv