Sergyeyev, Artur; Szablikowski, Błaẓej M. Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems. (English) Zbl 1227.37013 Phys. Lett., A 372, No. 47, 7016-7023 (2008). Summary: We introduce the cotangent universal hierarchy that extends the universal hierarchy from [L. Martínez Alonso and A. B. Shabat, Phys. Lett., A 300, No. 1, 58–64 (2002; Zbl 0997.37045); J. Nonlinear Math. Phys. 10, No. 2, 229–242 (2003; Zbl 1055.35092); Theor. Math. Phys. 140, No. 2, 1073-1085 (2004); translation from Teor. Mat. Fiz. 140, No. 2, 216–229 (2004; Zbl 1178.37067)] and [A. B. Shabat, Theor. Math. Phys. 136, No. 2, 1066–1076 (2003); translation from Teor. Mat. Fiz. 136, No. 2, 197–208 (2003; Zbl 1178.37091); J. Nonlinear Math. Phys. 12, Suppl. 1, 614 (2005)]. Then we construct a (2+1)-dimensional double central extension of the cotangent universal hierarchy and show that this extension is bi-Hamiltonian. This yields, as a byproduct, the central extension of the original universal hierarchy. Cited in 1 ReviewCited in 11 Documents MSC: 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 19C09 Central extensions and Schur multipliers 70H05 Hamilton’s equations Keywords:cotangent universal hierarchy; central extension; integrable systems; (2+1)-dimensional bi-Hamiltonian systems; \(R\)-matrix PDF BibTeX XML Cite \textit{A. Sergyeyev} and \textit{B. M. Szablikowski}, Phys. Lett., A 372, No. 47, 7016--7023 (2008; Zbl 1227.37013) Full Text: DOI arXiv References: [1] Martínez Alonso, L.; Shabat, A.B., Phys. lett. A, 300, 1, 58, (2002) · Zbl 0997.37045 [2] Shabat, A.B., Theor. math. phys., 136, 1066, (2003) [3] Martínez Alonso, L.; Shabat, A.B., J. nonlinear math. phys., 10, 2, 229, (2003) [4] Martínez Alonso, L.; Shabat, A.B., Theor. math. phys., 140, 2, 1073, (2004) [5] Shabat, A., J. nonlinear math. phys., 12, Suppl. 1, 614, (2005) [6] Takhtajan, L.A.; Faddeev, L.D., Hamiltonian methods in the theory of solitons, (1987), Springer Berlin · Zbl 1327.39013 [7] Reiman, A.G.; Semenov-Tyan-Shanskii, M.A., Dokl. akad. nauk SSSR, 251, 6, 1310, (1980), (in Russian) [8] Reiman, A.G.; Semenov-Tyan-Shanskii, M.A., J. math. sci., 31, 6, 3399, (1985) [9] Reyman, A.G.; Semenov-Tian-Shansky, M.A., Phys. lett. A, 130, 456, (1988) [10] Błaszak, M.; Szum, A., J. math. phys., 42, 1, 225, (2001) [11] Błaszak, M.; Szablikowski, B.M., J. phys. A: math. gen., 35, 10345, (2002) [12] Kupershmidt, B.A., J. nonlinear math. phys., 8, 363, (2001) [13] Ovsienko, V.; Roger, C., Commun. math. phys., 273, 357, (2007) [14] Ovsienko, V. [15] Dunajski, M.; Grant, J.D.E.; Strachan, I.A.B., J. math. phys., 48, 093502, (2007) [16] Santini, P.M.; Fokas, A.S., Commun. math. phys., 115, 375, (1988) [17] Fokas, A.S.; Santini, P.M., Math. phys., 116, 449, (1988) [18] Dorfman, I.Ya.; Fokas, A.S., J. math. phys., 33, 2504, (1992) [19] Zakharov, V.E.; Konopelchenko, B.G., Commun. math. phys., 94, 483, (1984) [20] Pavlov, M.V., J. math. phys., 44, 4134, (2003) [21] Ferapontov, E.V.; Khusnutdinova, K.R., Commun. math. phys., 248, 187, (2004) [22] Ferapontov, E.V.; Khusnutdinova, K.R., J. math. phys., 45, 2365, (2004) [23] Dunajski, M., J. geom. phys., 50, 126, (2004) [24] Manakov, S.V.; Santini, P.M., Theor. math. phys., 152, 1004, (2007) [25] Dunajski, M., J. phys. A: math. theor., 41, 315202, (2008) [26] Ferapontov, E.V., Phys. lett. A, 158, 112, (1991) [27] Mikhailov, A.V.; Yamilov, R.I., J. phys. A: math. gen., 31, 6707, (1998) [28] Olver, P.J., Applications of Lie groups to differential equations, (2000), Springer New York · Zbl 0937.58026 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.