A unified inverse scattering transformation for the local and nonlocal nonautonomous Gross-Pitaevskii equations

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. Published by AIP Publishing.