Abstract
We present the inverse scattering transformation for a nonisospectral AKNS hierarchy in which the spectral parameter is determined by an ordinary differential equation with polynomial nonlinearity, and thus, we give a unified treatment for the local and nonlocal nonautonomous Gross-Pitaevskii equations which possess the parity-time (PT) symmetric invariance. We find that unlike the local case, the PT-symmetry of the nonlocal Gross-Pitaevskii equation allows two different choices of the symmetry relations of the eigenfunctions which guarantee two different kinds of inverse scattering solutions.
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