Nonlinear Dynamics

, Volume 87, Issue 4, pp 2171–2177 | Cite as

Dark spatiotemporal optical solitary waves in self-defocusing nonlinear media

Original Paper


Dark three-dimensional spatiotemporal solitons or the “dark light bullets” in the self-defocusing nonlinear media with equal diffraction and dispersion lengths are demonstrated analytically. Our results show that the main characteristic of the dark light bullets can be described by the cylindrical Korteweg–de Vries (CKdV) equation. The dark wave packets are composed of the single-layer and multilayer toroidal rings. For the multilayer rings, there exist small inner rings enclosed in a large ring-shaped toroidal structure, when one chooses different orders of the soliton solutions of the CKdV equation. The radius of dark ring solitons increases with the propagation distance. Present results provide a feasible method for controlling the fundamental structure of these beams in the self-defocusing nonlinear media.


Dark spatiotemporal solitons Cylindrical Korteweg–de Vries equation Toroidal rings 



This work was supported by the National Natural Science Foundation of China (Project No. 61275001) and by the Natural Science Foundation of Guangdong Province, China (No. 2014A030313799). Work at the Texas A&M University at Qatar was supported by the NPRP 6-021-1-005 project with the Qatar National Research Fund (a member of Qatar Foundation). MRB also acknowledges support from the Al Sraiya Holding Group.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Wei-Ping Zhong
    • 1
    • 2
  • Milivoj R. Belić
    • 2
  • Yiqi Zhang
    • 3
  1. 1.Department of Electronic and Information EngineeringShunde PolytechnicShundeChina
  2. 2.Texas A&M University at QatarDohaQatar
  3. 3.Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic TechniqueXi’an Jiaotong UniversityXi’anChina

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