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

Yong Chen, Zhenya Yan*, Boris A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 Schrödinger 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.

Original languageEnglish
Article number133099
JournalPhysica D: Nonlinear Phenomena
Volume430
DOIs
StatePublished - Feb 2022

Funding

FundersFunder number
NSF of Jiangsu Higher Education Institutions of China11731014, 11925108, 19KJB110011
National Natural Science Foundation of China12001246, 11947087
Israel Science Foundation1286/17
Natural Science Foundation of Jiangsu ProvinceBK20190991

    Keywords

    • Adiabatic management
    • Higher-dimensional nonlinear Schrödinger equation
    • PT-symmetric potentials
    • Stable solitons

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