Two new discrete integrable systems |
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Authors: | Chen Xiao-Hong Zhang Hong-Qing |
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Affiliation: | a School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;b School of Science, University of Science and Technology Liaoning, Anshan 114051, China |
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Abstract: | In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra Â1. By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity. |
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Keywords: | discrete integrable system Hamiltonian structure loop algebra |
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