IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v143y2021ics096007792030878x.html

A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws

Author

Listed:
  • Çelik, Nisa
  • Seadawy, Aly R.
  • Sağlam Özkan, Yeşim
  • Yaşar, Emrullah

Abstract

In this study, we have dealt with a wave equation containing 4th order nonlinear mixed derivative. This model corresponds to solitary waves in nonlinear elastic circular rod. One dimensional optimal systems corresponding to Lie symmetry generator sub-algebras, symmetry reductions, and group invariant solutions corresponding to these systems have been systematically produced by Lie symmetry analysis of this model. In addition, traveling wave solutions were obtained with the help of an useful integration scheme of the model. These solutions are structures with physical properties of hyperbolic, trigonometric and rational solution types. Numerical simulations of the obtained solutions for different values of the parameters were made. The stability property of the obtained solutions is tested to show the ability of obtained solutions. In addition, the local conservation laws of the model were obtained with the help of the multiplier homotopy method.

Suggested Citation

  • Çelik, Nisa & Seadawy, Aly R. & Sağlam Özkan, Yeşim & Yaşar, Emrullah, 2021. "A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s096007792030878x
    DOI: 10.1016/j.chaos.2020.110486
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792030878X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110486?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. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    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. Nguyen, Thu Ha & Nguyen, Van Chung & Bui, Dang Quang & Dao, Phuong Nam, 2024. "An efficient Min/Max Robust Model Predictive Control for nonlinear discrete-time systems with dynamic disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 180(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. Tian, Yang & Tian, Hui & Cui, Qimei & Zhu, Xuzhen, 2024. "Phase transition phenomena in social propagation with dynamic fashion tendency and individual contact," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. 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).
    5. Aly R. Seadawy & Hanadi Zahed & Syed T. R. Rizvi, 2022. "Diverse Forms of Breathers and Rogue Wave Solutions for the Complex Cubic Quintic Ginzburg Landau Equation with Intrapulse Raman Scattering," Mathematics, MDPI, vol. 10(11), pages 1-22, May.
    6. Chaudry Masood Khalique & Karabo Plaatjie, 2021. "Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering," Mathematics, MDPI, vol. 10(1), pages 1-17, December.
    7. Xu, Zhihao & Lv, Zhiqiang & Chu, Benjia & Li, Jianbo, 2024. "A Fast Spatial-temporal Information Compression algorithm for online real-time forecasting of traffic flow with complex nonlinear patterns," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    8. Seadawy, Aly R. & Ahmed, Sarfaraz & Rizvi, Syed T.R. & Ali, Kashif, 2022. "Lumps, breathers, interactions and rogue wave solutions for a stochastic gene evolution in double chain deoxyribonucleic acid system," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

    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. Abdolamir Karbalaie & Hamed Hamid Muhammed & Bjorn-Erik Erlandsson, 2013. "Using Homo-Separation of Variables for Solving Systems of Nonlinear Fractional Partial Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-8, June.
    2. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. S. S. Nourazar & M. Habibi Matin & M. Simiari, 2011. "The HPM Applied to MHD Nanofluid Flow over a Horizontal Stretching Plate," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    4. Shweta, & Arora, Gourav & Kumar, Rajesh, 2025. "Large time solution for collisional breakage model: Laplace transformation based accelerated homotopy perturbation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 39-52.
    5. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    6. Abbasbandy, S., 2007. "A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 257-260.
    7. Javidi, M. & Golbabai, A., 2008. "Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 309-313.
    8. Alipanah, Amjad & Zafari, Mahnaz, 2023. "Collocation method using auto-correlation functions of compact supported wavelets for solving Volterra’s population model," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
    10. Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    11. Mohamed. Z. Mohamed & Mohammed Yousif & Amjad E. Hamza, 2022. "Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2022(1).
    12. Lv, Jian Cheng & Yi, Zhang, 2007. "Some chaotic behaviors in a MCA learning algorithm with a constant learning rate," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1040-1047.
    13. Xu, Lan, 2008. "Variational approach to solitons of nonlinear dispersive K(m,n) equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 137-143.
    14. Emad H. Aly & Abdelhalim Ebaid, 2013. "New Analytical and Numerical Solutions for Mixed Convection Boundary‐Layer Nanofluid Flow along an Inclined Plate Embedded in a Porous Medium," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    15. M. S. H. Chowdhury & I. Hashim & S. Momani & M. M. Rahman, 2012. "Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    16. Yu, Guo-Fu & Tam, Hon-Wah, 2006. "Conservation laws for two (2+1)-dimensional differential–difference systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 189-196.
    17. Moghimi, Mahdi & Hejazi, Fatemeh S.A., 2007. "Variational iteration method for solving generalized Burger–Fisher and Burger equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1756-1761.
    18. Mohamed S. Mohamed & Khaled A. Gepreel & Faisal A. Al-Malki & Nouf Altalhi, 2014. "Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    19. Keramati, B., 2009. "An approach to the solution of linear system of equations by He’s homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 152-156.
    20. Allan, Fathi M., 2009. "Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1744-1752.

    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:143:y:2021:i:c:s096007792030878x. 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.