New symmetries for the Ablowitz-Ladik hierarchies

Abstract

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.

arXiv comment11 pages

References in corpus (2)

• Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations
• Negative order MKdV hierarchy and a new integrable Neumann-like system

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• On a Second Discretization of the ZS-AKNS Spectral Problem: Revisit
• Symmetries for the Ablowitz-Ladik hierarchy: II. Integrable discrete nonlinear Schrödinger equation and discrete AKNS hierarchy