Geodesic
Integrability conditions for an analogue of the relativistic Toda chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 66-80 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a class of discrete-differential equations that contains the relativistic Toda chain and is characterized by one arbitrary function of six variables. We derive three conditions that allow testing the integrability of any given equation in this class. In deriving these conditions, we use higher symmetries distinguishing the equations that are integrable via the inverse scattering method.
Keywords: relativistic Toda chain, higher symmetry, integrability condition. 
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R. I. Yamilov. Integrability conditions for an analogue of the relativistic Toda chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 66-80. http://geodesic.mathdoc.fr/item/TMF_2007_151_1_a4/

[1] S. N. M. Ruijsenaars, Comm. Math. Phys., 133 (1990), 217–247 | DOI | MR | Zbl

[2] Yu. B. Suris, J. Phys. A, 30 (1997), 1745–1761 | DOI | MR | Zbl

[3] V. E. Adler, A. B. Shabat, TMF, 111 (1997), 323–334 | DOI | MR | Zbl

[4] V. V. Sokolov, A. B. Shabat, Sov. Sci. Rev. Sect. C, 4 (1984), 221–280 ; A. V. Mikhailov, A. B. Shabat, V. V. Sokolov, “The symmetry approach to classification of integrable equations”, What is Integrability?, ed. V. E. Zakharov, Springer, Berlin, 1991, 115–184 | MR | Zbl | DOI | MR | Zbl

[5] A. V. Mikhailov, A. B. Shabat, R. I. Yamilov, UMN, 42:4 (1987), 3–53 | DOI | MR | Zbl

[6] V. E. Adler, A. B. Shabat, R. I. Yamilov, TMF, 125 (2000), 355–424 | DOI | MR | Zbl

[7] R. I. Yamilov, UMN, 38:6 (1983), 155–156 ; R. I. Yamilov, “Classification of Toda type scalar lattices”, Nonlinear evolution equations and dynamical systems NEEDS{'}92, Proc. of the Eighth International Workshop (Dubna, Russia, 1992), eds. V. Makhankov, I. Puzynin, O. Pashaev, World Scientific, River Edge, NJ, 1993, 423–431 | MR

[8] D. Levi, R. Yamilov, J. Math. Phys., 38 (1997), 6648–6674 ; R. Yamilov, D. Levi, J. Nonlinear Math. Phys., 11 (2004), 75–101 | DOI | MR | Zbl | DOI | MR | Zbl

[9] R. Yamilov, J. Phys. A, 39 (2006), R541–R623 | DOI | MR | Zbl

[10] R. I. Yamilov, TMF, 139 (2004), 209–224 | DOI | MR | Zbl

[11] A. V. Mikhailov, A. B. Shabat, R. I. Yamilov, Comm. Math. Phys., 115 (1988), 1–19 | DOI | MR | Zbl