Nonlinear Dynamics

, Volume 79, Issue 1, pp 427–436 | Cite as

Sech-type and Gaussian-type light bullet solutions to the generalized (3\(+\)1)-dimensional cubic-quintic Schrödinger equation in \(\varvec{\mathcal {PT}}\)-symmetric potentials

  • Yi-Xiang Chen
Original Paper


We study two kinds of the generalized (3\(+\)1)-dimensional cubic-quintic Schrödinger equation in \(\mathcal {PT}\)-symmetric potentials and obtain two families (sech-type and Gaussian-type) and four kinds of analytical light bullet (LB) solutions. The stability of these solutions is tested by the linear stability analysis and the direct numerical simulation. Results imply that sech-type LB solutions are unstable for all parameters only in the extended Rosen–Morse potentials. Sech-type and Gaussian-type LB solutions are both stable below some thresholds for the imaginary part of other \(\mathcal {PT}\)-symmetric potentials in the defocusing cubic and focusing quintic medium, while they are always unstable for all parameters in other media. Moreover, we discuss the broadened and compressed behaviors of LBs in inhomogeneous hyperbolic system and periodic amplification system.


Light bullets Nonlinear Schrödinger equations  Cubic-quintic nonlinearity Broadened and compressed behaviors 



This work was supported by Zhejiang Province welfare project (Grant No. 2014C32006), the higher school visiting scholar development project (Grant No. FX2013103), the Zhejiang University of Media and Communications Research Fund (Grant No. ZC12XJY003) and National Natural Science Foundation of China (Grant No. 11374254).


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Electronics InformationZhejiang University of Media and CommunicationsHangzhouPeople’s Republic of China

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