Sato theory

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. 

 

 

KdV equation

\(K(x,t)=1+e^{2a(x-4a^2t+\delta)}\)

\(2(\frac{\partial^2}{\partial x^2})\log K(x,t)\)

\(K(x,t)=1+A_1e^{2a_1(x-4a_1^2t+\delta_1)}+A_2e^{2a_2(x-4a_2^2t+\delta_2)}+A_3e^{2a_1(x-4a_1^2t+\delta_1)+{2a_2(x-4a_2^2t+\delta_2)}\)

\(2(\frac{\partial^2}{\partial x^2})\log K(x,t)\)

 

 

Algebraic Geometrical Methods in Hamiltonian Mechanics http://www.jstor.org/stable/37539

 

 

 

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• Kadometsev-Petviashvii (KP hierarchy)

 

 

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. 
• Kajiwara, Kenji, Marta Mazzocco, 와/과Yasuhiro Ohta. 2007. “A remark on the Hankel determinant formula for solutions of the Toda equation”. Journal of Physics A: Mathematical and Theoretical 40 (42): 12661-12675. doi:10.1088/1751-8113/40/42/S11.
• Nakamura, Yoshimasa. 1994. “A tau-function of the finite nonperiodic Toda lattice”. Physics Letters A 195 (5-6) (12월 12): 346-350. doi:10.1016/0375-9601(94)90040-X.
• 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)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
    
  • http://blogsearch.google.com/blogsearch?q=
• http://ncatlab.org/nlab/show/HomePage

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/