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Bifurcation Analysis and Numerical Study of Wave Solution for Initial-Boundary Value Problem of the KdV-BBM Equation

Author

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  • Teeranush Suebcharoen

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand)

  • Kanyuta Poochinapan

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand)

  • Ben Wongsaijai

    (Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand)

Abstract

In this work, we study the bifurcation and the numerical analysis of the nonlinear Benjamin-Bona-Mahony-KdV equation. According to the bifurcation theory of a dynamic system, the various kinds of traveling wave profiles are obtained including the behavior of solitary and periodic waves. Additionally, a two-level linear implicit finite difference algorithm is implemented for investigating the Benjamin-Bona-Mahony-KdV model. The application of a priori estimation for the approximate solution also provides the convergence and stability analysis. It was demonstrated that the current approach is singularly solvable and that both time and space convergence are of second-order precision. To confirm the computational effectiveness, two numerical simulations are prepared. The findings show that the current technique performs admirably in terms of delivering second-order accuracy in both time and space with the maximum norm while outperforming prior schemes.

Suggested Citation

  • Teeranush Suebcharoen & Kanyuta Poochinapan & Ben Wongsaijai, 2022. "Bifurcation Analysis and Numerical Study of Wave Solution for Initial-Boundary Value Problem of the KdV-BBM Equation," Mathematics, MDPI, vol. 10(20), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3825-:d:943838
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    References listed on IDEAS

    as
    1. Kanyuta Poochinapan & Ben Wongsaijai & Thongchai Disyadej, 2014. "Efficiency of High-Order Accurate Difference Schemes for the Korteweg-de Vries Equation," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, December.
    2. Yiren Chen & Shaoyong Li & Mohammad Mirzazadeh, 2021. "New Traveling Wave Solutions and Interesting Bifurcation Phenomena of Generalized KdV-mKdV-Like Equation," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-6, November.
    3. You, Xiangcheng & Xu, Hang & Sun, Qiang, 2022. "Analysis of BBM solitary wave interactions using the conserved quantities," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Changna Lu & Qianqian Gao & Chen Fu & Hongwei Yang, 2017. "Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-11, November.
    5. Rouatbi, Asma & Omrani, Khaled, 2017. "Two conservative difference schemes for a model of nonlinear dispersive equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 516-530.
    6. He, Dongdong & Pan, Kejia, 2015. "A linearly implicit conservative difference scheme for the generalized Rosenau–Kawahara-RLW equation," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 323-336.
    7. Jiraporn Janwised & Ben Wongsaijai & Thanasak Mouktonglang & Kanyuta Poochinapan, 2014. "A Modified Three-Level Average Linear-Implicit Finite Difference Method for the Rosenau-Burgers Equation," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-11, April.
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