IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i18p2855-d1477915.html
   My bibliography  Save this article

Efficient Study on Westervelt-Type Equations to Design Metamaterials via Symmetry Analysis

Author

Listed:
  • Zehra Pinar Izgi

    (Department of Mathematics, Faculty of Arts and Science, Tekirdağ Namık Kemal University, 59030 Tekirdağ, Turkey)

  • Pshtiwan Othman Mohammed

    (Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq
    Research and Development Center, University of Sulaimani, Sulaymaniyah 46001, Iraq)

  • Ravi P. Agarwal

    (Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA)

  • Majeed A. Yousif

    (Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq)

  • Alina Alb Lupas

    (Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania)

  • Mohamed Abdelwahed

    (Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia)

Abstract

Metamaterials have emerged as a focal point in contemporary science and technology due to their ability to drive significant innovations. These engineered materials are specifically designed to couple the phenomena of different physical natures, thereby influencing processes through mechanical or thermal effects. While much of the recent research has concentrated on frequency conversion into electromagnetic waves, the field of acoustic frequency conversion still faces considerable technical challenges. To overcome these hurdles, researchers are developing metamaterials with customized acoustic properties. A key equation for modeling nonlinear acoustic wave phenomena is the dissipative Westervelt equation. This study investigates analytical solutions using ansatz-based methods combined with Lie symmetries. The approach presented here provides a versatile framework that is applicable to a wide range of fields in metamaterial design.

Suggested Citation

  • Zehra Pinar Izgi & Pshtiwan Othman Mohammed & Ravi P. Agarwal & Majeed A. Yousif & Alina Alb Lupas & Mohamed Abdelwahed, 2024. "Efficient Study on Westervelt-Type Equations to Design Metamaterials via Symmetry Analysis," Mathematics, MDPI, vol. 12(18), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2855-:d:1477915
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/18/2855/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/18/2855/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sahoo, S. & Ray, S. Saha, 2017. "Invariant analysis with conservation laws for the time fractional Drinfeld–Sokolov–Satsuma–Hirota equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 725-733.
    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. Musrrat Ali & Hemant Gandhi & Amit Tomar & Dimple Singh, 2023. "Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    2. Liu, Jian-Gen & Yang, Xiao-Jun & Feng, Yi-Ying & Cui, Ping, 2020. "On group analysis of the time fractional extended (2+1)-dimensional Zakharov–Kuznetsov equation in quantum magneto-plasmas," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 407-421.
    3. Sil, Subhankar & Raja Sekhar, T. & Zeidan, Dia, 2020. "Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 139(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:12:y:2024:i:18:p:2855-:d:1477915. 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.