"Sato theory"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
<h5>introduction</h5> | <h5>introduction</h5> | ||
| − | Sato’s Grassmannian and its determinant bundle became a “universal” setting where moduli spaces of curves (or maps or bundles) of arbitrary genus could<br> be mapped and made to interact | + | * Sato’s Grassmannian and its determinant bundle became a “universal” setting where moduli spaces of curves (or maps or bundles) of arbitrary genus could<br> be mapped and made to interact |
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| + | [[KdV equation]] | ||
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| + | <math>K(x,t)=1+e^{2a(x-4a^2t+\delta)}</math> | ||
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| + | <math>2(\frac{\partial^2}{\partial x^2})\log K(x,t)</math> | ||
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| + | <math>K(x,t)=1+A_1e^{2a_1(x-4a_1^2t+\delta_1)}+A_2e^{2a_2(x-4a_2^2t+\delta_2)}+A_3e^{2a_1(x-4a_1^2t+\delta_1)+{2a_2(x-4a_2^2t+\delta_2)}</math> | ||
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| + | <math>2(\frac{\partial^2}{\partial x^2})\log K(x,t)</math> | ||
| 14번째 줄: | 26번째 줄: | ||
<h5>related items</h5> | <h5>related items</h5> | ||
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| + | * [[Kadometsev-Petviashvii equation (KP equation)|Kadometsev-Petviashvii (KP hierarchy)]] | ||
2011년 3월 13일 (일) 12:26 판
introduction
- Sato’s Grassmannian and its determinant bundle became a “universal” setting where moduli spaces of curves (or maps or bundles) of arbitrary genus could
be mapped and made to interact
\(K(x,t)=1+e^{2a(x-4a^2t+\delta)}\)
\(2(\frac{\partial^2}{\partial x^2})\log K(x,t)\)
\(K(x,t)=1+A_1e^{2a_1(x-4a_1^2t+\delta_1)}+A_2e^{2a_2(x-4a_2^2t+\delta_2)}+A_3e^{2a_1(x-4a_1^2t+\delta_1)+{2a_2(x-4a_2^2t+\delta_2)}\)
\(2(\frac{\partial^2}{\partial x^2})\log K(x,t)\)
history
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- Discrete Integrable Systems http://dx.doi.org/10.1007/b94662
- Book review on Soliton equations and their algebro-geometric solutions. Vol. I. (1+1)-dimensional continuous models
- 2011년 books and articles
- http://library.nu/search?q=
- http://library.nu/search?q=
expositions
- Sato theory, p-adic tau function and arithmetic geometry
- Segal, Graeme, and George Wilson. 1985. Loop groups and equations of KdV type. Publications Mathématiques de L’Institut des Hautes Scientifiques 61, no. 1 (12): 5-65. doi:10.1007/BF02698802.
articles
- Eilbeck, J C, V Z Enolski, and J Gibbons. 2010. Sigma, tau and Abelian functions of algebraic curves. Journal of Physics A: Mathematical and Theoretical 43, no. 45 (11): 455216. doi:10.1088/1751-8113/43/45/455216.
- Eilbeck, J. C., V. Z. Enolski, S. Matsutani, Y. Onishi, and E. Previato. 2010. Abelian Functions for Trigonal Curves of Genus Three. International Mathematics Research Notices (7). doi:10.1093/imrn/rnm140. http://imrn.oxfordjournals.org/content/2007/rnm140.short.
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/10.1007/b94662
question and answers(Math Overflow)
blogs
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- http://ncatlab.org/nlab/show/HomePage
experts on the field