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Stability of Gaussian-type light bullets in the cubic-quintic-septimal nonlinear media with different diffractions under \({\mathcal {PT}}\)-symmetric potentials

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Abstract

From the governing equation \(-(3+1)\)-dimensional nonlinear Schrödinger equation with cubic-quintic-septimal nonlinearities, different diffractions and \({\mathcal {PT}}\)-symmetric potentials, we obtain two kinds of analytical Gaussian-type light bullet solutions. The septimal nonlinear term has a strong impact on the formation of light bullets. The eigenvalue method and direct numerical simulation to analytical solutions imply that stable and unstable evolution of light bullets against white noise attributes to the coaction of cubic-quintic-septimal nonlinearities, dispersion, different diffractions and \({\mathcal {PT}}\)-symmetric potential.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11375079).

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Authors and Affiliations

  1. College of Ecology, Lishui University, Lishui, 323000, Zhejiang, People’s Republic of China

    Hai-Ping Zhu

  2. College of Engineering and Design, Lishui University, Lishui, 323000, Zhejiang, People’s Republic of China

    Zhen-Huan Pan

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  1. Hai-Ping Zhu
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Correspondence to Hai-Ping Zhu.

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Zhu, HP., Pan, ZH. Stability of Gaussian-type light bullets in the cubic-quintic-septimal nonlinear media with different diffractions under \({\mathcal {PT}}\)-symmetric potentials. Nonlinear Dyn 89, 1745–1752 (2017). https://doi.org/10.1007/s11071-017-3549-3

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  • DOI: https://doi.org/10.1007/s11071-017-3549-3

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