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A hierarchy of Liouville integrable lattice equations and its integrable coupling systems

✍ Scribed by Lei-yu Tang; Jian-cong Fan; Xue-hua Li

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
247 KB
Volume
16
Category
Article
ISSN
1007-5704

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✦ Synopsis

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 by virtue of the trace identity. Furthermore, based on a discrete four-by-four matrix spectral problem, the discrete integrable coupling systems of the resulting hierarchy are obtained. Then, with the variational identity, the Hamiltonian structures of the obtained integrable coupling systems are established. Finally, the resulting Hamiltonian systems are proved to be all Liouville integrable.

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