Geodesic
On conservation laws in affine Toda systems
Vladikavkazskij matematičeskij žurnal, Tome 13 (2011) no. 1, pp. 59-70 Cet article a éte moissonné depuis la source Math-Net.Ru

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With the help of certain matrix decomposition and projectors of special forms we show that non-Abelian Toda systems associated with loop groups possess infinite sets of conserved quantities following from essentially different conservation laws. 
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M. S. Nirova. On conservation laws in affine Toda systems. Vladikavkazskij matematičeskij žurnal, Tome 13 (2011) no. 1, pp. 59-70. http://geodesic.mathdoc.fr/item/VMJ_2011_13_1_a6/

[1] Arnold V. I., Mathematical methods of classical mechanics, Graduate Texts in Mathematics, Springer-Verlag, Berlin, 1989, 536 pp. | DOI | MR

[2] Faddeev L. D., Takhtajan L. A., Hamiltonian methods in the theory of solitons, Springer Series in Soviet Math., Springer-Verlag, Berlin, 1987, 592 pp. | MR | Zbl

[3] Zakharov V. E., Shabat A. B., “Integration of nonlinear equations of mathematical physics by the inverse scattering method. II”, Funkt. Anal. Pril., 13 (1979), 13–22 (in Russian) | MR | Zbl

[4] Leznov A. N., Saveliev M. V., Group-theoretical methods for the integration of nonlinear dynamical systems, Progress in Physics, 15, Birkhauser Verlag, Berlin, 1992 | MR | Zbl

[5] Nirov Kh. S., Razumov A. V., “$W$-algebras for non-Abelian toda systems”, J. of Geometry and Physics, 48 (2003), 505–545, arXiv: hep-th/0210267 | DOI | MR | Zbl

[6] Mikhailov A. V., Shabat A. B., Yamilov R. I., “Symmetry approach to classification of nonlinear equations. Complete lists of integrable systems”, Russ. Math. Surv., 42:4 (1987), 1–63 | DOI | MR | Zbl

[7] Mikhailov A. V., Shabat A. B., Sokolov V. V., “The symmetry approach to classification of integrable equations”, What is Integrability?, Springer-Verlag, Berlin, 1991, 115–184 | DOI | MR | Zbl

[8] Mikhailov A. V., “The reduction problem and the inverse scattering method”, Physica D, 3 (1981), 73–117 | DOI | Zbl

[9] Nirov Kh. S., Razumov A. V., “On $\mathbb Z$-gradations of twisted loop Lie algebras of complex simple Lie algebras”, Commun. Math. Phys., 267 (2006), 587–610, arXiv: math-ph/0504038 | DOI | MR | Zbl

[10] Semenov-Tian-Shansky M. A., “Integrable systems and factorization problems”, Factorization and Integrable Systems, Birkhauser, Boston, 2003, 155–218, arXiv: nlin.si/0209057 | DOI | MR | Zbl

[11] Razumov A. V., Saveliev M. V., Lie algebras, geometry and Toda-type systems, Cambridge University Press, Cambridge, 1997 | MR | Zbl

[12] Razumov A. V., Saveliev M. V., “Maximally non-Abelian Toda systems”, Nucl. Phys. B, 494 (1997), 657–686, arXiv: hep-th/9612081 | DOI | MR | Zbl

[13] Razumov A. V., Saveliev M. V., “Multi-dimensional Toda-type systems”, Theor. Math. Phys., 112:2 (1997), 999–1022, arXiv: hep-th/9609031 | DOI | MR | Zbl

[14] Nirov Kh. S., Razumov A. V., “On classification of non-Abelian Toda systems”, Geometrical and Topological Ideas in Modern Physics, IHEP, Protvino, 2002, 213–221, arXiv: nlin.si/0305023

[15] Nirov Kh. S., Razumov A. V., “Toda equations associated with loop groups of complex classical Lie groups”, Nucl. Phys. B, 782 (2007), 241–275, arXiv: math-ph/0612054 | DOI | MR | Zbl

[16] Nirov Kh. S., Razumov A. V., “$\mathbb Z$-graded loop Lie algebras, loop groups, and Toda equations”, Theor. Math. Phys., 154:3 (2008), 385–404, arXiv: 0705.2681 | DOI | MR | Zbl