IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i7p1709-d1114839.html
   My bibliography  Save this article

Quiescent Optical Solitons for the Concatenation Model with Nonlinear Chromatic Dispersion

Author

Listed:
  • Yakup Yıldırım

    (Department of Computer Engineering, Biruni University, Istanbul 34010, Turkey)

  • Anjan Biswas

    (Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USA
    Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, Moscow 115409, Russia
    Department of Applied Sciences, Cross–Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201 Galati, Romania)

  • Luminita Moraru

    (Department of Chemistry, Physics and Environment, Faculty of Sciences and Environment, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania)

  • Abdulah A. Alghamdi

    (Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

This paper recovers quiescent optical solitons that are self-sustaining, localized wave packets that maintain their shape and amplitude over long distances due to a balance between nonlinearity and dispersion. When a soliton is in a state of quiescence, it means that it is stationary in both space and time. Quiescent optical solitons are typically observed in optical fibers, where nonlinearity and dispersion can lead to the formation of solitons. The concatenation model is considered to understand the behavior of optical pulses propagating through nonlinear media. Here, we consider the familiar nonlinear Schrödinger equation, the Lakshmanan–Porsezian–Daniel equation, and the Sasa–Satsuma equation. The current paper also addresses the model with nonlinear chromatic dispersion, a phenomenon that occurs in optical fibers and other dispersive media, where the chromatic dispersion of the material is modified by nonlinear effects. In the presence of nonlinearities, such as self-phase modulation and cross-phase modulation, the chromatic dispersion coefficient becomes a function of the optical intensity, resulting in nonlinear chromatic dispersion. A full spectrum of stationary optical solitons, along with straddled stationary solitons, are obtained. There are four integration schemes that made this retrieval possible. The numerical simulations are also included for these solitons. The parameter constraints also indicate the existence criteria for these quiescent solitons.

Suggested Citation

  • Yakup Yıldırım & Anjan Biswas & Luminita Moraru & Abdulah A. Alghamdi, 2023. "Quiescent Optical Solitons for the Concatenation Model with Nonlinear Chromatic Dispersion," Mathematics, MDPI, vol. 11(7), pages 1-25, April.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1709-:d:1114839
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/7/1709/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/7/1709/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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).
    2. Malomed, B.A., 2022. "Multidimensional dissipative solitons and solitary vortices," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    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. Kudryashov, Nikolay A. & Kutukov, Aleksandr A. & Biswas, Anjan & Zhou, Qin & Yıldırım, Yakup & Alshomrani, Ali Saleh, 2023. "Optical solitons for the concatenation model: Power-law nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Çelik, Nisa & Tetik, Duygu, 2024. "New dynamical analysis of the exact traveling wave solutions to a (3+1)-dimensional Gardner-KP equation by three efficient architecture," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. Anjan Biswas & Jose Vega-Guzman & Yakup Yıldırım & Luminita Moraru & Catalina Iticescu & Abdulah A. Alghamdi, 2023. "Optical Solitons for the Concatenation Model with Differential Group Delay: Undetermined Coefficients," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    4. Silambarasan, Rathinavel & Nisar, Kottakkaran Sooppy, 2023. "Doubly periodic solutions and non-topological solitons of 2+1− dimension Wazwaz Kaur Boussinesq equation employing Jacobi elliptic function method," Chaos, Solitons & Fractals, Elsevier, vol. 175(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. Dong, Liangwei & Fan, Mingjing & Malomed, Boris A., 2024. "Stable higher-order vortex quantum droplets in an annular potential," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    2. Anjan Biswas & Jose Vega-Guzman & Yakup Yıldırım & Luminita Moraru & Catalina Iticescu & Abdulah A. Alghamdi, 2023. "Optical Solitons for the Concatenation Model with Differential Group Delay: Undetermined Coefficients," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    3. Kudryashov, Nikolay A., 2024. "Solitons of the complex modified Korteweg–de Vries hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    4. Kudryashov, Nikolay A. & Kutukov, Aleksandr A. & Biswas, Anjan & Zhou, Qin & Yıldırım, Yakup & Alshomrani, Ali Saleh, 2023. "Optical solitons for the concatenation model: Power-law nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    5. Hanqing Zhao & Boris A. Malomed & Ivan I. Smalyukh, 2023. "Topological solitonic macromolecules," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    6. Djazet, Alain & Fewo, Serge I. & Djoko, Martin & Felenou, E. Tchomgo & Kofané, Timoléon C., 2023. "Extension of the stability criterion for dissipative vector solitons of a laser coupled two-dimensional Ginzburg–Landau Equation generated from vector asymmetric inputs," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Wang, Qing & Zhu, Junying & Wang, Jun & Yu, Haiyan & Hu, Beibei, 2024. "Controllable trajectory and shape of Hermite-Gaussian soliton clusters," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    8. Chen, Zhiming & Liu, Xiuye & Xie, Hongqiang & Zeng, Jianhua, 2024. "Three-dimensional Bose–Einstein gap solitons in optical lattices with fractional diffraction," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    9. Mahfoudi, Narimene & Bouguerra, Abdesselam & Triki, Houria & Azzouzi, Faiçal & Biswas, Anjan & Yıldırım, Yakup & Alshomrani, Ali Saleh, 2024. "Chirped self-similar optical solitons with cubic–quintic–septic–nonic form of self-phase modulation," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    10. Li, Chunyan & Konotop, Vladimir V. & Malomed, Boris A. & Kartashov, Yaroslav V., 2023. "Bound states in Bose-Einstein condensates with radially-periodic spin-orbit coupling," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    11. Liu, Dongshuai & Gao, Yanxia & Fan, Dianyuan & Zhang, Lifu, 2023. "Higher-charged vortex solitons in harmonic potential," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    12. Xu, Yinshen & Li, Peixin & Mihalache, Dumitru & He, Jingsong, 2023. "Resonant collisions among multi-breathers in the Mel’nikov system," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    13. Al-Marzoug, S.M. & Baizakov, B.B. & Bahlouli, H., 2023. "Two-dimensional symbiotic solitons and quantum droplets in a quasi-one-dimensional optical lattice," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    14. Manoj Mishra & Kirti Meena & Divya Yadav & Brajraj Singh & Soumendu Jana, 2023. "The dynamics, stability and modulation instability of Gaussian beams in nonlocal nonlinear media," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-13, August.
    15. Díaz, P. & Molinares, H. & Pérez, L.M. & Laroze, D. & Bragard, J. & Malomed, B.A., 2024. "Stable semivortex gap solitons in a spin–orbit-coupled Fermi gas," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    16. Wang, Qing & Zhou, Liangliang & Zhu, Junying & He, Jun-Rong, 2024. "Multi-vortex beams in nonlinear media with harmonic potential wells," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    17. Ding, Cui-Cui & Zhou, Qin & Xu, Si-Liu & Sun, Yun-Zhou & Liu, Wen-Jun & Mihalache, Dumitru & Malomed, Boris A., 2023. "Controlled nonautonomous matter–wave solitons in spinor Bose–Einstein condensates with spatiotemporal modulation," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    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. Liu, Dongshuai & Gao, Yanxia & Fan, Dianyuan & Zhang, Lifu, 2023. "Transformation of rotating dipole and vortex solitons in an anharmonic potential," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    20. Cao, Na & Yin, XiaoJun & Bai, ShuTing & LiYangXu,, 2023. "Breather wave, lump type and interaction solutions for a high dimensional evolution model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

    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:gam:jmathe:v:11:y:2023:i:7:p:1709-:d:1114839. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.