Sato theory
http://bomber0.myid.net/ (토론)님의 2011년 4월 17일 (일) 16:09 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 - tau function = the section of a determinant line bundle over an infinite-dimensional Grassmannian
- Matsutani, Shigeki. 2000. Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions. nlin/0007001 (July 1). doi:doi:10.1088/0305-4470/34/22/312. http://arxiv.org/abs/nlin/0007001.
\(K(x,t)=1+e^{2a(x-4a^2t+\delta)}\)
\(2(\frac{\partial^2}{\partial x^2})\log K(x,t)\)
\(K(x,t)=1+A_1e^{2a_1(x-4a_1^2t+\delta_1)}+A_2e^{2a_2(x-4a_2^2t+\delta_2)}+A_3e^{2a_1(x-4a_1^2t+\delta_1)+{2a_2(x-4a_2^2t+\delta_2)}\)
\(2(\frac{\partial^2}{\partial x^2})\log K(x,t)\)
Algebraic Geometrical Methods in Hamiltonian Mechanics http://www.jstor.org/stable/37539
Wronskian determinant
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.
- Poppe, C. 1989. “General determinants and the tau function for the Kadomtsev-Petviashvili hierarchy”. Inverse Problems 5 (4): 613-630. doi:10.1088/0266-5611/5/4/012.
- Freeman, N. C., 와/과J. J. C. Nimmo. 1983. “Soliton solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili equations: The wronskian technique”. Physics Letters A 95 (1) (4월 11): 1-3. doi:10.1016/0375-9601(83)90764-8
- http://dx.doi.org/10.1088/0266-5611/5/4/012
question and answers(Math Overflow)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field