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imported>Pythagoras0 잔글 (찾아 바꾸기 – “* Princeton companion to mathematics(Companion_to_Mathematics.pdf)” 문자열을 “” 문자열로) |
imported>Pythagoras0 |
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* http://en.wikipedia.org/wiki/ | * http://en.wikipedia.org/wiki/ | ||
* http://mathworld.wolfram.com/HirotaEquation.html | * http://mathworld.wolfram.com/HirotaEquation.html | ||
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* Yoshimasa matsuno Bilinear Transformation Method | * 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 |
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==expositions== | ==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 |
* [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 | + | * Goldstein, P. P. 2007. “Hints on the Hirota Bilinear Method.” Acta Physica Polonica A 112 (December): 1171. |
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[[분류:integrable systems]] | [[분류:integrable systems]] | ||
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[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 11월 18일 (월) 07:50 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.