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

• Chen, Junchao, Yong Chen, Bao-Feng Feng, Ken-ichi Maruno, and Yasuhiro Ohta. “An Integrable Semi-Discretization of the Coupled Yajima--Oikawa System.” arXiv:1509.06996 [math-Ph, Physics:nlin], September 21, 2015. http://arxiv.org/abs/1509.06996.
• Delisle, Laurent. “A N=2 Extension of the Hirota Bilinear Formalism and the Supersymmetric KdV Equation.” arXiv:1509.03137 [hep-Th, Physics:math-Ph], September 10, 2015. http://arxiv.org/abs/1509.03137.
• Bai, Yong-Qiang, and Yan-Jun LV. “Bilinear B"acklund Transformations and Lax Pair for the Boussinesq Equation.” arXiv:1412.1910 [nlin], December 5, 2014. http://arxiv.org/abs/1412.1910.
• 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.