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Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems. (English) Zbl 1227.37013
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.

MSC:
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
19C09 Central extensions and Schur multipliers
70H05 Hamilton’s equations
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