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The Liouville integrability of integrable couplings of Volterra lattice equation

โœ Scribed by Qiu-lan Zhao; Xi-Xiang Xu; Xin-Yue Li

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
243 KB
Volume
15
Category
Article
ISSN
1007-5704

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โœฆ Synopsis

A hierarchy of integrable couplings of Volterra lattice equations with three potentials is proposed, which is derived from a new discrete six-by-six matrix spectral problem. Moreover, by means of the discrete variational identity on semi-direct sums of Lie algebra, the two Hamiltonian forms are deduced for each lattice equation in the resulting hierarchy. A strong symmetry operator of the resulting hierarchy is given. Finally, we prove that the hierarchy of the resulting Hamiltonian equations are all Liouville integrable discrete Hamiltonian systems.

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A new discrete two-by-two matrix spectral problem with two potentials is introduced, followed by a hierarchy of integrable lattice equations obtained through discrete zero curvature equations. It is shown that the Hamiltonian structures of the resulting integrable lattice equations are established b