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A non-isospectral Lax pair is first introduced from which a kind ofnon-isospectral integrable TD hierarchy is derived, whose reduction is anintegrable system called the non-isospectral integrable TD system. Then byusing the inverse scattering transform (IST) method, new general solitonsolutions for the non-isospectral integrable TD hierarchy are obtained. Becausewe investigate soliton solutions of non-isospectral integrable systems by theIST method, a new Gel'fand-Levitan-Marchenko (GLM) equation needs to beconstructed. Finally, we explicitly obtain the exact solutions of thenon-isospectral integrable TD system. The method presented in the paper can beextensively applied to other integrable equations.

The general solutions for a non-isospectral integrable TD hierarchy via the inverse scattering transform