IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v169y2023ics0960077923001133.html

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

Author

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

Abstract

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.

Suggested Citation

  • Soltani, Mourad & Triki, Houria & Azzouzi, Faiçal & Sun, Yunzhou & Biswas, Anjan & Yıldırım, Yakup & Alshehri, Hashim M. & Zhou, Qin, 2023. "Pure–quartic optical solitons and modulational instability analysis with cubic–quintic nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001133
    DOI: 10.1016/j.chaos.2023.113212
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923001133
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113212?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhou, Qin & Triki, Houria & Xu, Jiakun & Zeng, Zhongliang & Liu, Wenjun & Biswas, Anjan, 2022. "Perturbation of chirped localized waves in a dual-power law nonlinear medium," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Andrea Blanco-Redondo & C. Martijn de Sterke & J.E. Sipe & Thomas F. Krauss & Benjamin J. Eggleton & Chad Husko, 2016. "Pure-quartic solitons," Nature Communications, Nature, vol. 7(1), pages 1-9, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mandeng, Lucien Mandeng & Zanga, Dieudonné & Djob, Roger Bertin, 2026. "Quartic-dispersion-induced modulational instability in coupled nonlinear Chen–Lee–Liu systems," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Jia-Hao & Qin, Huan-Qi & Si, Zhi-Zeng & Jia, Yun-Hao & Kudryashov, Nikolay A. & Wang, Yue-Yue & Dai, Chao-Qing, 2024. "Pure-quartic soliton attracted state and multi-soliton molecules in mode-locked fiber lasers," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    2. Mann, Nikita & Rani, Setu & Kumar, Sachin & Kumar, Raj, 2024. "Novel closed-form analytical solutions and modulation instability spectrum induced by the Salerno equation describing nonlinear discrete electrical lattice via symbolic computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 473-490.
    3. Kengne, Emmanuel, 2026. "Engineering optical quartic solitons embedded on a nonvanishing continuous-wave background in weakly birefringent fibers," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    4. Luo, Min & Wei, Yong & Luo, Liang & Jin, Jia-Hong & Kong, Yu-Jie & Zhou, Jun-Jie & Liu, Zhi-Yong & Tang, Shuang-Hong & Yin, Tian & Chen, Yue-Xin & Wang, Wen-Jin, 2025. "Dynamics of soliton collapse in dissipative pure-quartic soliton laser," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    5. Chen, Yu & Lü, Xing, 2025. "PINN-wf: A PINN-based algorithm for data-driven solution and parameter discovery of the Hirota equation appearing in communications and finance," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    6. Ze-Xian Zhang & Min Luo & Jia-Hao Liu & Yi-Tao Yang & Ti-Jian Li & Meng Liu & Ai-Ping Luo & Wen-Cheng Xu & Zhi-Chao Luo, 2024. "Coherence-controlled chaotic soliton bunch," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    7. Yang, Song & Zhu, Zhiwei & He, Chaojian & Qi, Yaoyao & Lin, Xuechun, 2024. "Pure-quartic soliton self-frequency shift in a mode-locked fiber laser," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    8. Justin Widjaja & Y. Long Qiang & Amelie F. J. Skelton & Lasse H. H. Sweetland & Antoine F. J. Runge & Christopher J. Lustri & C. Martijn de Sterke, 2025. "Observation of the universality of nonlinear mode coupling in a fibre laser," Nature Communications, Nature, vol. 16(1), pages 1-8, December.
    9. Mandeng, Lucien Mandeng & Zanga, Dieudonné & Djob, Roger Bertin, 2026. "Quartic-dispersion-induced modulational instability in coupled nonlinear Chen–Lee–Liu systems," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).
    10. Triki, Houria & Sun, Yunzhou & Zhou, Qin & Biswas, Anjan & Yıldırım, Yakup & Alshehri, Hashim M., 2022. "Dark solitary pulses and moving fronts in an optical medium with the higher-order dispersive and nonlinear effects," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    11. Lan, Wen-Zhi & Zhang, Jia-Hao & Dai, Tian-Le & Liu, Wen-Jun & Dai, Chao-Qing, 2025. "Energy-increasing driven hierarchical transition of weakly dissipative pure-sextic soliton to multi-breather soliton molecules," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    12. Chen, Yi-Xiang, 2023. "Vector peregrine composites on the periodic background in spin–orbit coupled Spin-1 Bose–Einstein condensates," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    13. Li, Li & Yu, Fajun, 2024. "The fourth-order dispersion effect on the soliton waves and soliton stabilities for the cubic-quintic Gross–Pitaevskii equation," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    14. Dai, Jiaxin & Zeng, Jiali & Hu, Wei & Lu, Daquan, 2022. "The bound states of pure-quartic solitons," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    15. Cao, Qi-Hao & Geng, Kai-Li & Zhu, Bo-Wei & Wang, Yue-Yue & Dai, Chao-Qing, 2023. "Scalar vortex solitons and vector dipole solitons in whispering gallery mode optical microresonators," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    16. Luo, Min & Zhang, Ze-Xian & Wei, Yong & Luo, Liang & Wang, Wen-Jin & Kong, Yu-Jie & Tang, Yu-Yan & Liu, Can & Li, Jun-Hao & Jin, Jia-Hong, 2025. "Pure-quartic soliton pulsating and creeping dynamics in a bidirectional mode-locked fiber laser," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    17. Liu, Congcong & He, Jiangyong & Wang, Shihai & Li, Jin & Ning, Yu & Wang, Pan & Liu, Yange & Wang, Zhi, 2025. "Spatiotemporal dynamics of dissipative solitons in anomalous dispersion few-mode fiber lasers," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    18. Zeng, Liangwei & Belić, Milivoj R. & Mihalache, Dumitru & Zhu, Xing, 2024. "Elliptical and rectangular solitons in media with competing cubic–quintic nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    19. Lee, Fang C. & dos Santos, Mateus C.P. & Avelar, Ardiley T. & Cardoso, Wesley B., 2026. "Influence of fourth-order dispersion on the formation of localized states in systems with inhomogeneous defocusing nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    20. Li, Jiawei & Zhang, Yanpeng & Zeng, Jianhua, 2022. "Dark gap solitons in one-dimensional nonlinear periodic media with fourth-order dispersion," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001133. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.