"Hirota bilinear method"의 두 판 사이의 차이
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* [http://users.utu.fi/hietarin/Bangalore.pdf Hirota’s bilinear method and integrability] Jarmo Hietarinta, 2008 | * [http://users.utu.fi/hietarin/Bangalore.pdf 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. | * Goldstein, P. P. 2007. “Hints on the Hirota Bilinear Method.” Acta Physica Polonica A 112 (December): 1171. | ||
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| + | * 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. | ||
[[분류:integrable systems]] | [[분류:integrable systems]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
2014년 8월 30일 (토) 18:41 판
introduction
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
계산 리소스
encyclopedia
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.