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Analysis of BBM solitary wave interactions using the conserved quantities

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  • You, Xiangcheng
  • Xu, Hang
  • Sun, Qiang

Abstract

In this paper, a simple, robust, fast and effective method based on the conserved quantities is developed to approximate and analyse the shape, structure and interaction characters of the solitary waves described by the Benjamin–Bona–Mahony (BBM) equation. Due to the invariant character of the conserved quantities, there is no need to solve the related complex nonlinear partial differential BBM equation to simulate the interactions between the solitary waves at the most merging instance. Good accuracy of the proposed method has been found when compared with the numerical method for the solitary wave interactions with different initial incoming wave shapes. The conserved quantity method developed in this work can serve as an ideal tool to benchmark numerical solvers, to perform the stability analysis, and to analyse the interacting phenomena between solitary waves.

Suggested Citation

  • You, Xiangcheng & Xu, Hang & Sun, Qiang, 2022. "Analysis of BBM solitary wave interactions using the conserved quantities," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010791
    DOI: 10.1016/j.chaos.2021.111725
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    References listed on IDEAS

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    1. Salupere, A. & Engelbrecht, J. & Peterson, P., 2003. "On the long-time behaviour of soliton ensembles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(1), pages 137-147.
    2. Yang, Yanhong & Wang, Yushun & Song, Yongzhong, 2018. "A new local energy-preserving algorithm for the BBM equation," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 119-130.
    3. Li, Meng & Zhao, Yong-Liang, 2018. "A fast energy conserving finite element method for the nonlinear fractional Schrödinger equation with wave operator," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 758-773.
    4. Seydi Battal Gazi Karakoç & Turgut Ak & Halil Zeybek, 2014. "An Efficient Approach to Numerical Study of the MRLW Equation with B-Spline Collocation Method," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-15, July.
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    Cited by:

    1. 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.

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