Pure–quartic optical solitons and modulational instability analysis with cubic–quintic nonlinearity

Mourad Soltani, Houria Triki, Faiçal Azzouzi, Yunzhou Sun*, Anjan Biswas, Yakup Yıldırım, Hashim M. Alshehri, Qin Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We analyze the propagation dynamics of intense light pulses in an optical medium exhibiting cubic–quintic nonlinearity and pure fourth-order dispersion. We show that this physical system may support a rich variety of periodic wave solutions in the presence of all physical processes. Interestingly, in the long-wave limit, two different types of quartic dark solitons with equal amplitudes and wave numbers but different widths are identified for the first time. The obtained dark soliton solutions are shown to be independent of any free parameters and their characteristics are uniquely determined by system parameters. The numerical examples are presented for illustrating the soliton evolution dynamics in the waveguiding system. The formation of these quartic dark solitons occurs in normal pure fourth-order dispersion when the quintic and cubic nonlinearities are competitive. The modulational instability of a continuous wave is also analyzed under the combined effects of quartic dispersion and cubic–quintic nonlinearities. Additionally, the role of quintic nonlinearity and fourth-order dispersion effects on the modulational instability has been discussed.

Original languageEnglish
Article number113212
JournalChaos, Solitons and Fractals
Publication statusPublished - Apr 2023
Externally publishedYes


  • Cubic–quintic nonlinearity
  • Dark solitons
  • Pure–quartic dispersion


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