Nonlinear Dynamics

, Volume 87, Issue 3, pp 1675–1683 | Cite as

Dynamics of light bullets in inhomogeneous cubic-quintic-septimal nonlinear media with \({\varvec{{\mathcal {PT}}}}\)-symmetric potentials

  • Chao-Qing Dai
  • Rui-Pin Chen
  • Yue-Yue Wang
  • Yan Fan
Original Paper


A (3+1)-dimensional nonlinear Schrödinger equation with variable-coefficient dispersion/diffraction and cubic-quintic-septimal nonlinearities is studied, two families of analytical light bullet solutions with two types of \({{\mathcal {PT}}}\)-symmetric potentials are obtained. The coefficient of the septimal nonlinear term strongly influences the form of light bullet. The direct numerical simulation indicates that light bullet solutions in different cubic-quintic-septimal nonlinear media exhibit different property of stability, and under different \({\mathcal {PT}}\)-symmetric potentials they also show different stability against white noise. These stabilities of evolution originate from subtle interplay among dispersion, diffraction, nonlinearity and \({\mathcal {PT}}\)-symmetric potential. Moreover, compression and expansion of light bullets in the hyperbolic dispersion/diffraction system and periodic modulation system are investigated numerically. The evolution of light bullet in periodic modulation system is more stable than that in the hyperbolic dispersion/diffraction system.


Cubic-quintic-septimal nonlinearity \({\mathcal {PT}}\)-symmetric potential Light bullet Compression and expansion 



This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LY17F050011 and LY17A040011), the National Natural Science Foundation of China (Grant Nos. 11375007, 11574271 and 11404289). Dr. Chao-Qing Dai is also sponsored by the Foundation of New Century “151 Talent Engineering” of Zhejiang Province of China and Youth Top-notch Talent Development and Training Program of Zhejiang A&F University. Dr. Rui-Pin Chen is also sponsored by the Science Research Foundation of Zhejiang Sci-Tech University (ZSTU) under Grant No. 14062078-Y.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Chao-Qing Dai
    • 1
  • Rui-Pin Chen
    • 2
  • Yue-Yue Wang
    • 1
  • Yan Fan
    • 1
  1. 1.School of SciencesZhejiang A&F UniversityLin’anPeople’s Republic of China
  2. 2.Department of Physics Zhejiang Sci-Tech UniversityHangzhouPeople’s Republic of China

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