In this paper, we introduce a class of novel --hyperbolic-function potentials composed of the Dirac and hyperbolic functions, supporting fully real energy spectra in the non-Hermitian Hamiltonian. The threshold curves of symmetry breaking are numerically presented. Moreover, in the self-focusing and defocusing Kerr-nonlinear media, the -symmetric potentials can also support the stable peakons, keeping the total power and quasi-power conserved. The unstable -symmetric peakons can be transformed into other stable peakons by the excitations of potential parameters. Continuous families of additional stable numerical peakons can be produced in internal modes around the exact peakons (even unstable). Further, we find that the stable peakons can always propagate in a robust form, remaining trapped in the slowly moving potential wells, which opens the way for manipulations of optical peakons. Other significant characteristics related to exact peakons, such as the interaction and power flow, are elucidated in detail. These results will be useful in explaining the related physical phenomena and designing the related physical experiments.
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February 2022
Research Article|
February 16 2022
Stability and modulation of optical peakons in self-focusing/defocusing Kerr nonlinear media with -δ-hyperbolic-function potentials
Yong Chen
;
Yong Chen
1
School of Mathematics and Statistics, Jiangsu Normal University
, Xuzhou 221116, China
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Jin Song;
Jin Song
2
Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
, Beijing 100190, China
3
School of Mathematical Sciences, University of Chinese Academy of Sciences
, Beijing 100049, China
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Xin Li;
Xin Li
4
School of Mathematics and Statistics, Changshu Institute of Technology
, Changshu 215500, China
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Zhenya Yan
Zhenya Yan
a)
2
Key Lab of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
, Beijing 100190, China
3
School of Mathematical Sciences, University of Chinese Academy of Sciences
, Beijing 100049, China
a)Author to whom correspondence should be addressed: zyyan@mmrc.iss.ac.cn
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a)Author to whom correspondence should be addressed: zyyan@mmrc.iss.ac.cn
Chaos 32, 023122 (2022)
Article history
Received:
December 01 2021
Accepted:
January 28 2022
Citation
Yong Chen, Jin Song, Xin Li, Zhenya Yan; Stability and modulation of optical peakons in self-focusing/defocusing Kerr nonlinear media with -δ-hyperbolic-function potentials. Chaos 1 February 2022; 32 (2): 023122. https://doi.org/10.1063/5.0080485
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