Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schr\"odinger equations

• URL: http://arxiv.org/abs/2111.09482v1
• Date: Thu, 18 Nov 2021 02:25:52 GMT
• Title: Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schr\"odinger equations
• Authors: Yong Chen, Zhenya Yan, Boris A. Malomed
• Abstract summary: PT-symmetric generalized Scarf-II (GS-II) potentials can support exact solitons in one- and multi-dimensional nonlinear Schr"odinger equation. continuous families of fundamental and higher-order solitons are produced. stable solitons can always propagate, in a robust form, remaining trapped in slowly moving potential wells.
• Score: 2.8331714502894396
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Schr\"odinger 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 adibatic 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 relative physical experiments.

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