A Unified Inverse Scattering Transformation for the Local and Nonlocal Nonautonomous Gross-Pitaevskii Equations
Document Type
Article
Publication Date
2017
Digital Object Identifier (DOI)
https://doi.org/10.1063/1.4974772
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" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px 2px 0px 0px; margin: 0px; position: relative;">š¯’«š¯’ÆPT) symmetric invariance. We find that unlike the local case, the PT" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px 2px 0px 0px; margin: 0px; position: relative;">š¯’«š¯’ÆPT-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.
Was this content written or created while at USF?
Yes
Citation / Publisher Attribution
Journal of Mathematical Physics, v. 58, issue 1, art. 013505
Scholar Commons Citation
Zhang, Yu-Juan; Zhao, Dun; and Ma, Wen-Xiu, "A Unified Inverse Scattering Transformation for the Local and Nonlocal Nonautonomous Gross-Pitaevskii Equations" (2017). Mathematics and Statistics Faculty Publications. 154.
https://digitalcommons.usf.edu/mth_facpub/154
