Geodesic
The Elliptic Gaudin System with Spin
Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 3, pp. 426-441 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the algebraic-geometric structure of the elliptic Gaudin two-puncture model previously obtained. We identify this system with the system of pole dynamics of finite-gap solutions of the matrix Davey–Stewartson equation. We also obtain the action-angle variables and construct explicit solutions of this system in terms of theta functions. We discuss the geometry of degenerations of this system. 
@article{TMF_2002_130_3_a3,
     author = {D. V. Talalaev},
     title = {The {Elliptic} {Gaudin} {System} with {Spin}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {426--441},
     year = {2002},
     volume = {130},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_130_3_a3/}
}
TY  - JOUR
AU  - D. V. Talalaev
TI  - The Elliptic Gaudin System with Spin
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 426
EP  - 441
VL  - 130
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_130_3_a3/
LA  - ru
ID  - TMF_2002_130_3_a3
ER  - 
%0 Journal Article
%A D. V. Talalaev
%T The Elliptic Gaudin System with Spin
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 426-441
%V 130
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2002_130_3_a3/
%G ru
%F TMF_2002_130_3_a3
D. V. Talalaev. The Elliptic Gaudin System with Spin. Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 3, pp. 426-441. http://geodesic.mathdoc.fr/item/TMF_2002_130_3_a3/

[1] I. M. Krichever, “Nelineinye uravneniya i ellipticheskie krivye”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 23, ed. R. V. Gamkrelidze, VINITI, M., 1983, 79–136 | MR

[2] A. Gorsky, I. Krichever, A. Marshakov, A. Mironov, A. Morozov, Integrability and Seiberg–Witten exact solution, E-print hep-th/9505035 | MR

[3] R. Donagi, E. Witten, Nucl. Phys. B, 460 (1996), 299–334 | DOI | MR | Zbl

[4] I. Krichever, O. Babelon, E. Billey, M. Talon, Am. Math. Soc. Transl., 170:2 (1995), 83–119 | MR | Zbl

[5] I. M. Krichever, A. V. Zabrodin, UMN, 50:6 (1995), 3–56 | MR | Zbl

[6] N. Nekrasov, Commun. Math. Phys., 180 (1996), 587–604 ; E-print hep-th/9503157 | DOI | MR

[7] B. Enriquez, V. Rubtsov, Hitchin systems, higher Gaudin operators and $r$-matrices, E-print alg-geom/9503010 | MR

[8] N. Hitchin, Duke Math. J, 54:1 (1987), 91–114 | DOI | MR | Zbl

[9] B. van Geemen, E. Previato, Duke Math. J., 85 (1996), 659–684 | DOI | MR

[10] K. Gawedzki, P. Tran-Ngoc-Bich, J. Math. Phys., 41 (2000), 4695–4712 | DOI | MR | Zbl

[11] T. M. Malanyuk, UMN, 46:5 (1991), 171–172 | MR

[12] D. Talalaev, J. Math. Phys., 6:4 (1999), 471–492 | MR

[13] I. M. Krichever, D. H. Phong, J. Diff. Geom., 45 (1997), 349–389 | DOI | MR | Zbl

[14] I. M. Krichever, D. H. Phong, Symplectic forms in the theory of solitons, E-print hep-th/9708170 | MR

[15] I. Krichever, Elliptic solutions to difference non-linear equations and nested Bethe Ansatz equation, E-print solv-int/9804016 | MR

[16] B. Enriquez, B. Feigin, V. Rubtsov, Separation of variables for Gaudin–Calogero systems, E-print q-alg/9605030 | MR

[17] D. V. Talalaev, $R$-matrichnyi podkhod v zadachakh konechnozonnogo integrirovaniya, Diss. ...kand. f.-m. n., MGU, M., 2000; http://wwwth.itep.ru/mathphys/people/talalaev/phd.htm

[18] T. Brzeziński, Dynamical $r$-matrices and separation of variables: the generalized Calogero–Moser model, E-print hep-th/9401049 | MR

[19] M. Olshanetsky, Lett. Math. Phys., 42 (1997), 59–71 | DOI | MR | Zbl