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

 

 

related items

• KdV equation
• bilinear mathematics

 

 

계산 리소스

• https://docs.google.com/file/d/0B8XXo8Tve1cxVjBqOGE1OU00VkU/edit

 

encyclopedia

• http://en.wikipedia.org/wiki/
• http://mathworld.wolfram.com/HirotaEquation.html

 

 

books

• Yoshimasa matsuno Bilinear Transformation Method
• Hietarinta, J. 1997. “Introduction to the Hirota Bilinear Method.” In Integrability of Nonlinear Systems, edited by Y. Kosmann-Schwarzbach, B. Grammaticos, and K. M. Tamizhmani, 95–103. Lecture Notes in Physics 495. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0113694. http://arxiv.org/abs/solv-int/9708006

 

expositions

• Satsuma, J. 2004. “Bilinear Formalism in Soliton Theory.” In Integrability of Nonlinear Systems, edited by Yvette Kosmann-Schwarzbach, K. M. Tamizhmani, and Basil Grammaticos, 251–268. Lecture Notes in Physics 638. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/978-3-540-40962-5_8
• Hirota’s bilinear method and integrability Jarmo Hietarinta, 2008
• Goldstein, P. P. 2007. “Hints on the Hirota Bilinear Method.” Acta Physica Polonica A 112 (December): 1171.

articles

• Bazeia, D., L. Losano, and J. L. R. Santos. “Solitonic Traveling Waves in Galileon Theory.” arXiv:1408.3822 [hep-Th, Physics:math-Ph], August 17, 2014. http://arxiv.org/abs/1408.3822.