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In this article, the Darboux transformation for the non-isospectral AKNShierarchy is constructed. We show that the Darboux transformation for thenon-isospectral AKNS hierarchy is not an auto-B\"acklund transformation,because the integral constants of the hierarchy will be changed after thetransformation. The transform rule of the integral constants will be alsoderived. By this means, the soliton solutions of the nonlinear equationsderived by the non-isospectral AKNS hierarchy can be found.

Darboux Transformation for the Non-isospectral AKNS Hierarchy and Its Asymptotic Property