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