IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v220y2024icp341-356.html
   My bibliography  Save this article

Behavior of analytical schemes with non-paraxial pulse propagation to the cubic–quintic nonlinear Helmholtz equation

Author

Listed:
  • Chen, Haiying
  • Shahi, Adele
  • Singh, Gurpreet
  • Manafian, Jalil
  • Eslami, Baharak
  • Alkader, Naief Alabed

Abstract

In this paper, the cubic–quintic nonlinear Helmholtz equation which enables a pulse propagates in a planar waveguide with Kerr-like and quintic nonlinearities is studied. By noticing that the system is a non-integrable one, we could to get the diverse of solitary wave solutions by using standard tan(ϕ/2)-expansion technique and the exp(−Ω(η))-Expansion scheme. In particular, four forms of function solution including soliton, bright soliton, singular soliton, periodic wave solutions are investigated. To achieve this, an illustrative example of the Helmholtz equation is provided to demonstrate the feasibility and reliability of the procedure used in this study. The effect of the free parameters on the behavior of acquired figures to some solutions of two nonlinear exact cases was also analyzed due to the nature of nonlinearities. The dynamic properties of the obtained results are shown and analyzed by some density, two and three-dimensional images. We believe that our results will be a way for future research generating optical memories based on the non-paraxial solitons.

Suggested Citation

  • Chen, Haiying & Shahi, Adele & Singh, Gurpreet & Manafian, Jalil & Eslami, Baharak & Alkader, Naief Alabed, 2024. "Behavior of analytical schemes with non-paraxial pulse propagation to the cubic–quintic nonlinear Helmholtz equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 341-356.
  • Handle: RePEc:eee:matcom:v:220:y:2024:i:c:p:341-356
    DOI: 10.1016/j.matcom.2024.02.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424000429
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2024.02.003?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Xiuwang Wang & Jalil Manafian & Wayan Eka Mahendra & Azher M. Abed & Mustafa Z. Mahmoud & Guizhen Liang & Wen-Xiu Ma, 2022. "Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-20, May.
    2. Zeng, Liangwei & Mihalache, Dumitru & Malomed, Boris A. & Lu, Xiaowei & Cai, Yi & Zhu, Qifan & Li, Jingzhen, 2021. "Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Cai, Wei & Mohammaditab, Rasoul & Fathi, Gholamreza & Wakil, Karzan & Ebadi, Abdol Ghaffar & Ghadimi, Noradin, 2019. "Optimal bidding and offering strategies of compressed air energy storage: A hybrid robust-stochastic approach," Renewable Energy, Elsevier, vol. 143(C), pages 1-8.
    4. Ahmadou Moustapha Diop & Jean-Luc Polleux & Catherine Algani & Said Mazer & Mohammed Fattah & Moulhime EL Bekkali, 2023. "Design electrical model noise and perform nonlinearities of SiGe bipolar phototransistor," International Journal of Innovative Research and Scientific Studies, Innovative Research Publishing, vol. 6(4), pages 731-740.
    5. Kalsoom Sherazi & Naveed Sheikh & Misbah Anjum & Arbab Ghulam Raza, 2023. "Solar drying experimental research and mathematical modelling of wild mint and peach moisture content," Journal of Asian Scientific Research, Asian Economic and Social Society, vol. 13(2), pages 94-107.
    6. Sakkaravarthi, K. & Johnpillai, A.G. & Durga Devi, A. & Kanna, T. & Lakshmanan, M., 2018. "Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 457-472.
    7. Deffo, Guy Roger & Yamgoué, Serge Bruno & Pelap, François Beceau, 2021. "Bifurcation of solitary and periodic waves of an extended cubic-quintic Schrödinger equation with nonlinear dispersion effects governing modulated waves in a bandpass inductor-capacitor network," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    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. Khater, Mostafa M.A., 2022. "Nonparaxial pulse propagation in a planar waveguide with Kerr–like and quintic nonlinearities; computational simulations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Liu, Lijun & Qian, Jin & Hua, Li & Zhang, Bin, 2022. "System estimation of the SOFCs using fractional-order social network search algorithm," Energy, Elsevier, vol. 255(C).
    3. Arnous, Ahmed H. & Biswas, Anjan & Yıldırım, Yakup & Zhou, Qin & Liu, Wenjun & Alshomrani, Ali S. & Alshehri, Hashim M., 2022. "Cubic–quartic optical soliton perturbation with complex Ginzburg–Landau equation by the enhanced Kudryashov’s method," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Sun, Xianke & Wang, Gaoliang & Xu, Liuyang & Yuan, Honglei & Yousefi, Nasser, 2021. "Optimal estimation of the PEM fuel cells applying deep belief network optimized by improved archimedes optimization algorithm," Energy, Elsevier, vol. 237(C).
    5. Cheng, Shen & Zhao, Gaiju & Gao, Ming & Shi, Yuetao & Huang, Mingming & Yousefi, Nasser, 2021. "Optimal hybrid energy system for locomotive utilizing improved Locust Swarm optimizer," Energy, Elsevier, vol. 218(C).
    6. Yu, Binbin & Li, Jianjing & Liu, Che & Sun, Bo, 2022. "A novel short-term electrical load forecasting framework with intelligent feature engineering," Applied Energy, Elsevier, vol. 327(C).
    7. Wu, Cong & Li, Jiaxuan & Liu, Wenjin & He, Yuzhe & Nourmohammadi, Samad, 2023. "Short-term electricity demand forecasting using a hybrid ANFIS–ELM network optimised by an improved parasitism–predation algorithm," Applied Energy, Elsevier, vol. 345(C).
    8. 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).
    9. Hannes Wallimann & David Imhof & Martin Huber, 2023. "A Machine Learning Approach for Flagging Incomplete Bid-Rigging Cartels," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1669-1720, December.
    10. Lu, Xiaohui & Li, Bing & Guo, Lin & Wang, Peifang & Yousefi, Nasser, 2021. "Exergy analysis of a polymer fuel cell and identification of its optimum operating conditions using improved Farmland Fertility Optimization," Energy, Elsevier, vol. 216(C).
    11. Wang, Xinlin & Flores, Robert & Brouwer, Jack & Papaefthymiou, Marios, 2022. "Real-time detection of electrical load anomalies through hyperdimensional computing," Energy, Elsevier, vol. 261(PA).
    12. Sriyakul, Thanaporn & Jermsittiparsert, Kittisak, 2021. "Risk-controlled economic performance of compressed air energy storage and wind generation in day-ahead, intraday and balancing markets," Renewable Energy, Elsevier, vol. 165(P1), pages 182-193.
    13. Li, Ruiheng & Tian, Hao & Di, Yi & Hossain, Sarmistha, 2024. "Nonlinear simulating of the Proton Exchange Membrane Fuel Cells utilizing Ridgelet Neural Network optimized using a hybrid form of Northern Goshawk Optimizer," Applied Energy, Elsevier, vol. 360(C).
    14. Wu, Danman & Bai, Jiayu & Wei, Wei & Chen, Laijun & Mei, Shengwei, 2021. "Optimal bidding and scheduling of AA-CAES based energy hub considering cascaded consumption of heat," Energy, Elsevier, vol. 233(C).
    15. Bai, Jiayu & Liu, Feng & Xue, Xiaodai & Wei, Wei & Chen, Laijun & Wang, Guohua & Mei, Shengwei, 2021. "Modelling and control of advanced adiabatic compressed air energy storage under power tracking mode considering off-design generating conditions," Energy, Elsevier, vol. 218(C).
    16. Hu, Xiang & Yin, Zhixiang, 2022. "A study of the pulse propagation with a generalized Kudryashov equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    17. Li, Bingkang & Zhao, Huiru & Wang, Xuejie & Zhao, Yihang & Zhang, Yuanyuan & Lu, Hao & Wang, Yuwei, 2022. "Distributionally robust offering strategy of the aggregator integrating renewable energy generator and energy storage considering uncertainty and connections between the mid-to-long-term and spot elec," Renewable Energy, Elsevier, vol. 201(P1), pages 400-417.
    18. Wensheng Chen & Jalil Manafian & Khaled Hussein Mahmoud & Abdullah Saad Alsubaie & Abdullah Aldurayhim & Alabed Alkader, 2023. "Cutting-Edge Analytical and Numerical Approaches to the Gilson–Pickering Equation with Plenty of Soliton Solutions," Mathematics, MDPI, vol. 11(16), pages 1-35, August.
    19. Ren, Xiaojun & Wu, Yongtang & Hao, Dongmin & Liu, Guoxu & Zafetti, Nicholas, 2021. "Analysis of the performance of the multi-objective hybrid hydropower-photovoltaic-wind system to reduce variance and maximum power generation by developed owl search algorithm," Energy, Elsevier, vol. 231(C).
    20. Al-Kalbani, Kaltham K. & Al-Ghafri, K.S. & Krishnan, E.V. & Biswas, Anjan, 2021. "Solitons and modulation instability of the perturbed Gerdjikov–Ivanov equation with spatio-temporal dispersion," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).

    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:220:y:2024:i:c:p:341-356. 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.