Geodesic
Equations of motion and conserved quantities in non-Abelian discrete integrable models
Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 1, pp. 34-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conserved quantities for the Hirota bilinear difference equation, which is satisfied by eigenvalues of the transfer matrix, are studied. The transfer-matrix eigenvalue combinations that are integrals of motion for discrete integrable models, which correspond to $A_{k-1}$ algebras and satisfy zero or quasi-periodic boundary conditions, are found. Discrete equations of motion for a non-Abelian generalization of the Liouville model and the discrete analogue of the Tsitseiko equation are obtained. 
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V. A. Verbus; A. P. Protogenov. Equations of motion and conserved quantities in non-Abelian discrete integrable models. Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 1, pp. 34-46. http://geodesic.mathdoc.fr/item/TMF_1999_119_1_a2/

[1] Al. B. Zamolodchikov, Nucl. Phys., 342 (1990), 695 | DOI | MR

[2] A. Klümper, P. Pearce, Physica A, 183 (1992), 304 | DOI | MR | Zbl

[3] A. Kuniba, T. Nakanishi, J. Suzuki, Int. J Mod. Phys. A, 9 (1994), 5215 | DOI | MR | Zbl

[4] F. Ravanini, A. Valleriani, R. Tateo, Int. J. Mod. Phys. A, 8 (1993), 1707 | DOI | MR

[5] P. B. Wiegmann, Int. J. Mod. Phys. B, 11 (1997), 75 | DOI | MR | Zbl

[6] A. Zabrodin, Bethe ansatz and classical Hirota equations, E-print hep-th/9607162 | MR

[7] I. Krichever, P. Wiegmann, A. Zabrodin, Elliptic solutions to difference non-linear equations and related many-body problems, E-print hep-th/9704090 | MR

[8] O. Lipan, P. Wiegmann, A. Zabrodin, Fusion rules for quantum transfer matrices as a dynamical system on Grassmann manifolds, E-print solv-int/9704015 | MR

[9] Y. B. Suris, J. Phys. A, 29 (1996), 451 | DOI | MR | Zbl

[10] F. W. Nijhoff, O. Ragnisco, V. B. Kuznetsov, Commun. Math. Phys., 176 (1996), 681 | DOI | MR | Zbl

[11] H. W. Capel, F. W. Nijhoff, “Integrable lattice equations”, Important Developments in Soliton Theory, eds. A. S. Fokas, V. E. Zakharov, Springer, Berlin–Heidelberg–New York, 1993, 38 | DOI | MR | Zbl

[12] A. V. Zabrodin, TMF, 113 (1997), 179 | DOI | MR

[13] I. Krichever, O. Lipan, P. Wiegmann, A. Zabrodin, Quantum integrable systems and elliptic solutions of classical discrete nonlinear equations, , 1996 E-print hep-th/9604080 | MR

[14] I. G. Korepanov, Vacuum curves, classical integrable systems in discrete space-time and statistical physics, E-print hep-th/9312197

[15] L. D. Faddeev, “How algebraic Bethe ansatz works for integrable model”, Quantum Symmetries, Les Houches Lectures, Session LXIV, eds. A. Connes, K. Gawedzki, and J. Zinn-Justin, North-Holland, Amsterdam, 1998, 149 ; E-print hep-th/9605187 | MR | Zbl

[16] V. Bazhanov, A. Bobenko, N. Reshetikhin, Commun. Math. Phys., 175 (1996), 377 | DOI | MR | Zbl

[17] D. Bernard, A. LeClair, Commun. Math. Phys., 142 (1991), 99 | DOI | MR | Zbl

[18] A. P. Protogenov, V. A. Verbus, Mod. Phys. Lett. B, 11 (1997), 283 | DOI

[19] A. Protogenov, Haldane's statistical interactions and universal properties of anyon systems, Preprint IC/95/26, ICTP, Trieste, 1995

[20] T. Fukui, N. Kawakami, Phys. Rev. B, 51 (1995), 5239 | DOI

[21] F. D. M. Haldane, Phys. Rev. Lett., 67 (1991), 937 | DOI | MR | Zbl

[22] B. Enrikes, B. L. Feigin, TMF, 103 (1995), 507

[23] L. A. Takhtadzhyan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[24] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov: Metod obratnoi zadachi, Nauka, M., 1980 | MR

[25] A. V. Zabrodin, Pisma v ZhETF, 66 (1997), 620 | MR

[26] S. Saito, N. Saitoh, Phys. Lett. A, 120 (1987), 1052 | DOI | MR

[27] R. Hirota, J. Phys. Soc. Japan, 56 (1987), 4285 | DOI | MR

[28] R. Hirota, J. Phys. Soc. Japan, 43 (1977), 2079 | DOI | MR | Zbl

[29] L. Faddeev, A. Volkov, Lett. Math. Phys., 32 (1994), 125 | DOI | MR | Zbl

[30] A. Volkov, Lett. Math. Phys., 39 (1997), 313 | DOI | MR | Zbl

[31] R. Jackiw, So-Young Pi, Progr. Theor. Phys. Suppl., 107 (1992), 1 | DOI | MR

[32] A. Bobenko, W. Schief, Discrete indefinite affine spheres, Preprint SFB288. V. 263, Technische Universität, Berlin, 1997 | MR