Hirota bilinear method

 

 

 

 

Advantages of the bilinear formalism:

• Multisoliton solutions easy to construct.
• The dependent variables are usually tau-functions, with good properties.
• Natural for the Sato theory, which explains hierarchies of integrable equations (Jimbo and Miwa)
• Suitable for classification: the bilinear form strongly restricts the freedom of changing dependent variables.

 

 

example

http://www.thehcmr.org/issue2_1/soliton.pdf

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• KdV equation

 

 

encyclopedia

• http://en.wikipedia.org/wiki/
• http://mathworld.wolfram.com/HirotaEquation.html
• http://www.scholarpedia.org/
• http://eom.springer.de
• http://www.proofwiki.org/wiki/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

 

books

• Jarmo Hietarinta: Introduction to the Hirota Bilinear Method, volume 638 of Lect. Notes Phys. New York: Springer-Verlag 2004.
• 2011년 books and articles
• http://library.nu/search?q=
• http://library.nu/search?q=

 

 

expositions

• Notes on solutions in Wronskian form to soliton equations: KdV-type, 2006
• Hirota’s bilinear method and integrability Jarmo Hietarinta, 2008
• Goldstein, P. P. 2007. “Hints on the Hirota Bilinear Method”. Acta Physica Polonica A 112 (12월 1): 1171. http://adsabs.harvard.edu/abs/2007AcPPA.112.1171G
• Introduction to the Hirota bilinear method  J. Hietarinta, 1997

 

 

articles

• Integrable deformations of CFTs and the discrete Hirota equations
  
  • Werner Nahm, Sinéad Keegan, 2009
    
• Ma, Wen-Xiu, and Yuncheng You. 2005. Solving the Korteweg-de Vries Equation by Its Bilinear Form: Wronskian Solutions. Transactions of the American Mathematical Society 357, no. 5 (May 1): 1753-1778. 

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question and answers(Math Overflow)

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experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/