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• W2094641320 abstract "In the paper, we first investigate symmetries of isospectral and non-isospectral four-potential Ablowitz–Ladik hierarchies. We express these hierarchies in the form of un,t= LmH(0), where m is an arbitrary integer (instead of a nature number) and L is the recursion operator. Then by means of the zero-curvature representations of the isospectral and non-isospectral flows, we construct symmetries for the isospectral equation hierarchy as well as non-isospectral equation hierarchy, respectively. The symmetries, respectively, form two centerless Kac-Moody-Virasoro algebras. The recursion operator L is proved to be hereditary and a strong symmetry for this isospectral equation hierarchy. Besides, we make clear for the relation between four-potential and two-potential Ablowitz–Ladik hierarchies. The even order members in the four-potential Ablowitz–Ladik hierarchies together with their symmetries and algebraic structures can be reduced to two-potential case. The reduction keeps invariant for the algebraic structures and the recursion operator for two potential case becomes L2." @default.
• W2094641320 created "2016-06-24" @default.
• W2094641320 creator A5069105446 @default.
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• W2094641320 date "2010-11-01" @default.
• W2094641320 modified "2023-09-26" @default.
• W2094641320 title "Symmetries for the Ablowitz-Ladik Hierarchy: Part I. Four-Potential Case" @default.
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• W2094641320 doi "https://doi.org/10.1111/j.1467-9590.2010.00493.x" @default.
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