IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v239y2026icp83-95.html

Three types of solitons propagating in saturable nonlinear media

Author

Listed:
  • Wang, Lihong
  • Chen, Tingting
  • He, Jingsong

Abstract

In this paper, we investigate the propagation of light pulses in nonlinear saturable optical media, focusing on the nonlinear Schrödinger equation (NLSE) characterized by a saturable nonlinearity. We employ a Madelung-type transformation to derive stationary solutions, resulting in three types of soliton solutions: peakon-like solutions, bright soliton, and dark peakon. Additionally, we explore the physical implications of the parameters governing the NLSE and conduct detailed stability analyses of the solitons utilizing the Vakhitov–Kolokolov stability criterion.

Suggested Citation

  • Wang, Lihong & Chen, Tingting & He, Jingsong, 2026. "Three types of solitons propagating in saturable nonlinear media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 83-95.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:83-95
    DOI: 10.1016/j.matcom.2025.05.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475425001934
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2025.05.010?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. Rabie, Wafaa B. & Ahmed, Hamdy M., 2022. "Construction cubic-quartic solitons in optical metamaterials for the perturbed twin-core couplers with Kudryashov's sextic power law using extended F-expansion method," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. D. R. Solli & C. Ropers & P. Koonath & B. Jalali, 2007. "Optical rogue waves," Nature, Nature, vol. 450(7172), pages 1054-1057, December.
    3. Calvo, Gabriel F. & Belmonte-Beitia, Juan & Pérez-García, Víctor M., 2009. "Exact bright and dark spatial soliton solutions in saturable nonlinear media," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1791-1798.
    Full references (including those not matched with items on IDEAS)

    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. Li, Liu-Qing & Gao, Yi-Tian & Yu, Xin & Ding, Cui-Cui & Wang, Dong, 2022. "Bilinear form and nonlinear waves of a (1+1)-dimensional generalized Boussinesq equation for the gravity waves over water surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 494-508.
    2. Li, Li & Yu, Fajun, 2025. "Some mixed soliton wave interaction patterns and stabilities for Rabi-coupled nonlocal Gross–Pitaevskii equations," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    3. Göksel, İzzet & Antar, Nalan & Bakırtaş, İlkay, 2018. "Two-dimensional solitons in cubic-saturable media with PT-symmetric lattices," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 83-89.
    4. Zhang, Yu & Li, Chuanzhong & He, Jingsong, 2016. "Rogue waves in a resonant erbium-doped fiber system with higher-order effects," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 826-841.
    5. Seadawy, Aly R. & Ali, Safdar & Rizvi, Syed T.R., 2022. "On modulation instability analysis and rogue waves in the presence of external potential: The (n + 1)-dimensional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Liu, Xue-Ke & Wang, Zhen & Du, Ruo-Chen & Wen, Xiao-Yong, 2025. "Rogue wave dynamics and energy spectra for the generalized Heisenberg spin chain equation," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    7. Xi-zhong Liu & Zhi-Mei Lou & Xian-Min Qian & Lamine Thiam, 2019. "A Study on Lump and Interaction Solutions to a (3 + 1)-Dimensional Soliton Equation," Complexity, Hindawi, vol. 2019, pages 1-12, October.
    8. Sang, Xue & Dong, Huanhe & Fang, Yong & Liu, Mingshuo & Kong, Yuan, 2024. "Soliton, breather and rogue wave solutions of the nonlinear Schrödinger equation via Darboux transformation on a time–space scale," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    9. Kudryashov, Nikolay A., 2025. "Painlevé test, first integrals and analytical solutions of the Korteweg–de Vries–Burgers equation with a nonlinear source," Chaos, Solitons & Fractals, Elsevier, vol. 201(P3).
    10. Li, Lingfei & Yan, Yongsheng & Xie, Yingying, 2022. "Rational solutions with non-zero offset parameters for an extended (3 + 1)-dimensional BKP-Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    11. Alexandra Völkel & Luca Nimmesgern & Adam Mielnik-Pyszczorski & Timo Wirth & Georg Herink, 2022. "Intracavity Raman scattering couples soliton molecules with terahertz phonons," Nature Communications, Nature, vol. 13(1), pages 1-6, December.
    12. Xu, Yun-Jie, 2023. "Vector ring-like combined Akhmediev breathers for partially nonlocal nonlinearity under external potentials," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    13. Wang, Tingyou & Qin, Zhenyun & Mu, Gui & Zheng, Fuzhuang & Qiao, Zhijun, 2025. "Rogue wave patterns associated with Adler–Moser polynomials in the nonlocal nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    14. Zhao, Yi-Di & Wang, Yu-Feng & Yang, Sheng-Xiong & Zhang, Xi & Chen, Yi-Xin, 2024. "Soliton, breather and rogue wave solutions of the higher-order modified Gerdjikov–Ivanov equation," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    15. Chen, Yi-Xiang, 2024. "(3+1)-dimensional partially nonlocal ring-like bright-dark monster waves," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    16. Zhang, Yi & Sun, YanBo & Xiang, Wen, 2015. "The rogue waves of the KP equation with self-consistent sources," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 204-213.
    17. Wei, Peng-Fei & Long, Chun-Xiao & Zhu, Chen & Zhou, Yi-Ting & Yu, Hui-Zhen & Ren, Bo, 2022. "Soliton molecules, multi-breathers and hybrid solutions in (2+1)-dimensional Korteweg-de Vries-Sawada-Kotera-Ramani equation," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    18. Yue-jun Deng & Rui-yu Jia & Ji Lin, 2019. "Lump and Mixed Rogue-Soliton Solutions of the (2 + 1)-Dimensional Mel’nikov System," Complexity, Hindawi, vol. 2019, pages 1-9, November.
    19. Jiang, Yan & Qu, Qi-Xing, 2021. "Solitons and breathers for a generalized nonlinear Schrödinger equation via the binary Bell polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 57-68.
    20. Shen, Yuan, 2025. "Dynamics of certain localized waves in an erbium-doped fiber system with the quintic terms," Chaos, Solitons & Fractals, Elsevier, vol. 192(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:matcom:v:239:y:2026:i:c:p:83-95. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.