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Optimal decay rates of the dissipative shallow water waves modeled by coupling the Rosenau-RLW equation and the Rosenau-Burgers equation with power of nonlinearity

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  • Wongsaijai, Ben
  • Poochinapan, Kanyuta

Abstract

This paper studies the asymptotic behavior of a solution of dispersive shallow water waves modeled by coupling the Rosenau-RLW equation and the Rosenau-Burgers equation. The energy decay rates of the solution to the model are examined through the Fourier transform method. Moreover, we develop a pseudo-compact finite difference scheme for solving the model, study solution behavior, and confirm our theoretical results. The fundamental energy-decreasing property, which is obtained from the model of coupling the Rosenau-RLW equation with the Rosenau-Burgers equation, is derived and preserved by the present numerical scheme. The existence, uniqueness, convergence, and stability of the numerical solution are theoretically analyzed. Some numerical experiments are also conducted to demonstrate the accuracy and robustness of the present method. Finally, to verify the optimal decay rates, the numerical results are carried out at variant time scales by applying the moving boundary technique. The simulations are successfully constructed to support the theoretical results.

Suggested Citation

  • Wongsaijai, Ben & Poochinapan, Kanyuta, 2021. "Optimal decay rates of the dissipative shallow water waves modeled by coupling the Rosenau-RLW equation and the Rosenau-Burgers equation with power of nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    • Handle: RePEc:eee:apmaco:v:405:y:2021:i:c:s0096300321002927
    DOI: 10.1016/j.amc.2021.126202
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    References listed on IDEAS

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    1. Jinsong Hu & Yulan Wang, 2013. "A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, November.
    2. 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.
    3. Atouani, Noureddine & Omrani, Khaled, 2015. "On the convergence of conservative difference schemes for the 2D generalized Rosenau–Korteweg de Vries equation," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 832-847.
    4. Jun Zhang & Zixin Liu & Fubiao Lin & Jianjun Jiao, 2019. "Asymptotic Analysis and Error Estimate for Rosenau-Burgers Equation," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, June.
    5. Wongsaijai, B. & Mouktonglang, T. & Sukantamala, N. & Poochinapan, K., 2019. "Compact structure-preserving approach to solitary wave in shallow water modeled by the Rosenau-RLW equation," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 84-100.
    6. 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.
    7. 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.
    8. Xintian Pan & Luming Zhang, 2012. "Numerical Simulation for General Rosenau-RLW Equation: An Average Linearized Conservative Scheme," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-15, May.
    9. 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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    Cited by:

    1. Mouktonglang, Thanasak & Yimnet, Suriyon & Sukantamala, Nattakorn & Wongsaijai, Ben, 2022. "Dynamical behaviors of the solution to a periodic initial–boundary value problem of the generalized Rosenau-RLW-Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 114-136.

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