Stability of Gaussian-type soliton in the cubic–quintic nonlinear media with fourth-order diffraction and \(\mathcal {PT}\)-symmetric potentials

  • Camus Gaston Latchio TiofackEmail author
  • Nathan Nkouessi Tchepemen
  • Alidou Mohamadou
  • Timoléon Crépin Kofané
Original paper


We report on the existence and stability of Gaussian-type soliton in the nonlinear Schrödinger (NLS) equation with interplay of cubic–quintic nonlinearity, fourth-order diffraction (FOD) and novel quartic anharmonic parity-time (\(\mathcal {PT}\))-symmetric Gaussian potential. We study numerically the impact of the FOD coefficient on the regions of unbroken/broken linear \(\mathcal {PT}\)-symmetric phases. In the nonlinear domain, we derive exact soliton solutions of the one-dimensional and two-dimensional cubic–quintic NLS equation with \(\mathcal {PT}\)-symmetric Gaussian potential and FOD coefficients. Moreover, the stability of the constructed soliton solution is investigated. The results of linear stability analysis are validated by comparison with numerical simulations. Furthermore, we also show that the relative strength of the FOD coefficient influences the direction of the power flow.


Fourth-order diffraction Cubic–quintic nonlinearities \(\mathcal {PT}\)-symmetric quartic Gaussian potential Gaussian soliton Stability 



C. G. L. Tiofack acknowledges the support of the “Laboratoire d’Excellence CEMPI: Centre Européen pour les Mathématiques, la Physique et leurs Interactions.” The authors would like to thank the anonymous reviewers for their useful and valuable comments and suggestions.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Laboratory of Mechanics, Department of Physics, Faculty of ScienceUniversity of Yaounde IYaoundéCameroon
  2. 2.Fundamental Physics Laboratory, Group of Nonlinear Physics and Complex Systems, Department of Physics, Faculty of ScienceUniversity of DoualaDoualaCameroon
  3. 3.Condensed Matter Laboratory, Department of Physics, Faculty of ScienceUniversity of MarouaMarouaCameroon
  4. 4.The Abdus Salam International Centre for Theoretical PhysicsTriesteItaly

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