"Sato theory"의 두 판 사이의 차이

2011년 4월 17일 (일) 16:09 판

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

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.

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

@@ 92번째 줄: / 92번째 줄: @@
 * 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:[http://dx.doi.org/10.1093/imrn/rnm140 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”. <em>Inverse Problems</em> 5 (4): 613-630. doi:[http://dx.doi.org/10.1088/0266-5611/5/4/012 10.1088/0266-5611/5/4/012].
-* Soliton-solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili equations
+*  Freeman, N. C., 와/과J. J. C. Nimmo. 1983. “Soliton solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili equations: The wronskian technique”. <em>Physics Letters A</em> 95 (1) (4월 11): 1-3. doi:[http://dx.doi.org/10.1016/0375-9601%2883%2990764-8 10.1016/0375-9601(83)90764-8]<br>  <br>
-* 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/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
 * http://dx.doi.org/10.1088/0266-5611/5/4/012