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Dynamical behaviors of the solution to a periodic initial–boundary value problem of the generalized Rosenau-RLW-Burgers equation

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  • Mouktonglang, Thanasak
  • Yimnet, Suriyon
  • Sukantamala, Nattakorn
  • Wongsaijai, Ben

Abstract

The behaviors of a solution to a periodic initial–boundary value problem (IBVP) for the generalized Rosenau-RLW-Burgers equation are analyzed in this paper. Under the smoothness of its initial value, the global existence and uniqueness of the solution to the periodic IBVP for the equation are proved by means of the continuation extension and L2-energy estimates. The impact of the viscous term on the equation for the behaviors of the global solution is theoretically investigated. More precisely, two types of nonlinear wave behaviors are dealt with; one is the exponential convergence of the global solution to the average of its initial value when the viscous term is nonzero, and the other is the oscillation of the global solution around the initial average at any given time when the viscous term vanishes. Additionally, numerical simulations are provided to illustrate and validate our theoretical results. Further, the effects of some parameters on the periodic IBVP for the generalized Rosenau-RLW-Burgers equation are discussed when proceeding with an initial Gaussian condition.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:114-136
    DOI: 10.1016/j.matcom.2022.01.004
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    References listed on IDEAS

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    1. 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).
    2. Yin, Xiao-Jun & Yang, Lian-Gui & Liu, Quan-Sheng & Su, Jin-Mei & Wu, Guo-rong, 2018. "Structure of equatorial envelope Rossby solitary waves with complete Coriolis force and the external source," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 68-74.
    3. 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.
    4. 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.
    5. Xie, Yingying & Li, Lingfei, 2022. "Multiple-order breathers for a generalized (3+1)-dimensional Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation near the offshore structure," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 19-31.
    6. Dimitrienko, Yu.I. & Li, Shuguang & Niu, Yi, 2021. "Study on the dynamics of a nonlinear dispersion model in both 1D and 2D based on the fourth-order compact conservative difference scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 661-689.
    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.
    8. 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.
    9. Lu, Changna & Fu, Chen & Yang, Hongwei, 2018. "Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 104-116.
    10. Huiping Cui, 2012. "The asymptotic behavior of solutions of an initial boundary value problem for the generalized Benjamin-Bona-Mahony equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 43(4), pages 323-342, August.
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