Title

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;">𝒫𝒯PT) 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;">𝒫𝒯PT-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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Citation / Publisher Attribution

Journal of Mathematical Physics, v. 58, issue 1, art. 013505

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