IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v190y2025ics0960077924012967.html
   My bibliography  Save this article

Bifurcation analysis and exact solutions of the conformable time fractional Symmetric Regularized Long Wave equation

Author

Listed:
  • Zhang, Jing
  • Zheng, Zhen
  • Meng, Hui
  • Wang, Zenggui

Abstract

This paper investigates exact solutions for the conformable time fractional Symmetric Regularized Long Wave equation by applying the bifurcation analysis method and the exp(−Φ(ξ))-expansion method. By analyzing the long behaviors of the exact solutions plotted in 3D and 2D figures, we can model weakly nonlinear ion acoustic and space-charge waves. The bifurcation of the equation is analyzed based on the condition where the first integral constant is zero and the second integral constant is not zero. Based on different parameter conditions, many phase portraits and exact solutions including dark soliton, bright soliton, breaking wave, periodic and singular solutions for the equation are obtained. It has been proven that bifurcation method provides a wider range of solutions compared with other methods. Then the exp(−Φ(ξ))−expansion method is utilized to get the more solutions. Next graphical representations are presented that show physical characteristics of the solutions and the significance of the methods for fractional partial differential equations. Finally, we make a comprehensive comparison with other literatures.

Suggested Citation

  • Zhang, Jing & Zheng, Zhen & Meng, Hui & Wang, Zenggui, 2025. "Bifurcation analysis and exact solutions of the conformable time fractional Symmetric Regularized Long Wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:chsofr:v:190:y:2025:i:c:s0960077924012967
    DOI: 10.1016/j.chaos.2024.115744
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924012967
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115744?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. Qinjun Li & Danyal Soybaş & Onur Alp Ilhan & Gurpreet Singh & Jalil Manafian, 2021. "Pure Traveling Wave Solutions for Three Nonlinear Fractional Models," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-18, April.
    2. Özkan Güner & Dursun Eser, 2014. "Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-8, July.
    3. Qinghao Zhu & Jianming Qi, 2022. "Exact Solutions of the Nonlinear Space‐Time Fractional Partial Differential Symmetric Regularized Long Wave (SRLW) Equation by Employing Two Methods," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    4. M. B. Almatrafi, 2023. "Construction Of Closed Form Soliton Solutions To The Space-Time Fractional Symmetric Regularized Long Wave Equation Using Two Reliable Methods," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-12.
    5. Ali, Khalid K. & Nuruddeen, R.I. & Raslan, K.R., 2018. "New structures for the space-time fractional simplified MCH and SRLW equations," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 304-309.
    6. Qinghao Zhu & Jianming Qi & Wen-Xiu Ma, 2022. "Exact Solutions of the Nonlinear Space-Time Fractional Partial Differential Symmetric Regularized Long Wave (SRLW) Equation by Employing Two Methods," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-20, May.
    7. Shalu Saini & Rajeev Kumar & Deeksha & Rishu Arora & Kamal Kumar, 2023. "Symmetry Analysis and Wave Solutions of the Fisher Equation Using Conformal Fractional Derivatives," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    8. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
    9. Özkan Güner & Dursun Eser, 2014. "Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    10. Wen, Zhenshu, 2020. "The generalized bifurcation method for deriving exact solutions of nonlinear space-time fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    11. Shalu Saini & Rajeev Kumar & Deeksha & Rishu Arora & Kamal Kumar & Tudor Barbu, 2023. "Symmetry Analysis and Wave Solutions of the Fisher Equation Using Conformal Fractional Derivatives," Journal of Applied Mathematics, Hindawi, vol. 2023, pages 1-10, September.
    12. Qinjun Li & Danyal Soybaş & Onur Alp Ilhan & Gurpreet Singh & Jalil Manafian, 2021. "Pure Traveling Wave Solutions for Three Nonlinear Fractional Models," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    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. Hesham G Abdelwahed & Reem Alotaibi & Emad K El-Shewy & Mahmoud A E Abdelrahman, 2024. "An insight into the stochastic solitonic features of the Maccari model using the solver technique," PLOS ONE, Public Library of Science, vol. 19(12), pages 1-9, December.
    2. Kudryashov, Nikolay A. & Zakharchenko, Anastasia S., 2014. "Painlevé analysis and exact solutions for the Belousov–Zhabotinskii reaction–diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 111-117.
    3. Eslami, Mostafa, 2016. "Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 141-148.
    4. Ahmed Salem & Lamya Almaghamsi, 2023. "Solvability of Sequential Fractional Differential Equation at Resonance," Mathematics, MDPI, vol. 11(4), pages 1-18, February.
    5. Kudryashov, N.A., 2015. "On nonlinear differential equation with exact solutions having various pole orders," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 173-177.
    6. Yusuf Pandir & Halime Ulusoy, 2013. "New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations," Journal of Mathematics, Hindawi, vol. 2013, pages 1-5, January.
    7. Oke Davies Adeyemo & Lijun Zhang & Chaudry Masood Khalique, 2022. "Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics," Mathematics, MDPI, vol. 10(14), pages 1-46, July.
    8. M. B. Almatrafi, 2024. "Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach," Mathematics, MDPI, vol. 13(1), pages 1-17, December.
    9. Innocent Simbanefayi & Chaudry Masood Khalique, 2020. "Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    10. Ali, Khalid K. & Cattani, Carlo & Gómez-Aguilar, J.F. & Baleanu, Dumitru & Osman, M.S., 2020. "Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    11. Kudryashov, Nikolay A. & Ivanova, Yulia S., 2016. "Painleve analysis and exact solutions for the modified Korteweg–de Vries equation with polynomial source," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 377-382.
    12. Fahmy, E.S., 2008. "Travelling wave solutions for some time-delayed equations through factorizations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1209-1216.
    13. Vitanov, Nikolay K. & Dimitrova, Zlatinka I. & Vitanov, Kaloyan N., 2015. "Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with applications," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 363-378.
    14. Tehrani, D. Haji Taghi & Solaimani, M., 2023. "Effects of the medium fractionality and oscillating potential profiles on the Superarrivals of the Gaussian wave packets," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    15. Mustafa Inc & Rubayyi T. Alqahtani & Ravi P. Agarwal, 2023. "W-Shaped Bright Soliton of the (2 + 1)-Dimension Nonlinear Electrical Transmission Line," Mathematics, MDPI, vol. 11(7), pages 1-13, April.
    16. Constantin Bota & Bogdan Căruntu & Dumitru Ţucu & Marioara Lăpădat & Mădălina Sofia Paşca, 2020. "A Least Squares Differential Quadrature Method for a Class of Nonlinear Partial Differential Equations of Fractional Order," Mathematics, MDPI, vol. 8(8), pages 1-12, August.
    17. 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.
    18. Yang, Lijuan & Du, Xianyun & Yang, Qiongfen, 2016. "New variable separation solutions to the (2 + 1)-dimensional Burgers equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1271-1275.
    19. Ramírez, J. & Romero, J.L. & Muriel, C., 2016. "Reductions of PDEs to second order ODEs and symbolic computation," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 122-136.
    20. Kudryashov, N.A. & Lavrova, S.F., 2021. "Dynamical features of the generalized Kuramoto-Sivashinsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(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:eee:chsofr:v:190:y:2025:i:c:s0960077924012967. 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.