New symmetries for the Ablowitz-Ladik hierarchies

Details New symmetries for the Ablowitz-Ladik hierarchies New symmetries for the Ablowitz-Ladik hierarchies

2006-01-26

arxiv.org/abs/nlin/0601056v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages

Scientific paper

10.1016/j.physleta.2006.06.077

In the letter we give new symmetries for the isospectral and non-isospectral Ablowitz-Ladik hierarchies by means of the zero curvature representations of evolution equations related to the Ablowitz-Ladik spectral problem. Lie algebras constructed by symmetries are further obtained. We also discuss the relations between the recursion operator and isospectral and non-isospectral flows. Our method can be generalized to other systems to construct symmetries for non-isospectral equations.

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