Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrodinger equations

We study a class of physically intriguing PT-symmetric generalized Scarf-II (GS-II) potentials, which can support exact solitons in one-and multi-dimensional nonlinear Schrodinger equation. In the 1D and multi-D settings, we find that a properly adjusted localization parameter may support fully real energy spectra. Also, continuous families of fundamental and higher-order solitons are produced. The fundamental states are shown to be stable, while the higher-order ones, including 1D multimodal solitons, 2D solitons, and 3D light bullets, are unstable. Further, we find that the stable solitons can always propagate, in a robust form, remaining trapped in slowly moving potential wells of the GS-II type, which opens the way for manipulations of optical solitons. Solitons may also be transformed into stable forms by means of adiabatic variation of potential parameters. Finally, an alternative type of n-dimensional PT-symmetric GS-II potentials is reported too. These results will be useful to further explore the higher-dimensional PT-symmetric solitons and to design the related physical experiments. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

We studied a class of physically intriguing PT-symmetric generalized Scarf-II (GS-II) potentials that can support exact solitons in one- and multi-dimensional nonlinear Schrodinger equation. In the 1D and multi-D settings, we found that a properly adjusted localization parameter may support fully real energy spectra. Continuous families of fundamental and higher-order solitons were produced. While the fundamental states were stable, the higher-order ones were unstable. The stable solitons were capable of robust propagation and remained trapped in slowly moving potential wells, which offers possibilities for manipulating optical solitons. Adiabatic variation of potential parameters could transform solitons into stable forms.