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On Solitary Wave Solutions for the Camassa‐Holm and the Rosenau‐RLW‐Kawahara Equations with the Dual‐Power Law Nonlinearities

Author

Listed:
  • Nattakorn Sukantamala
  • Supawan Nanta

Abstract

The nonlinear wave equation is a significant concern to describe wave behavior and structures. Various mathematical models related to the wave phenomenon have been introduced and extensively being studied due to the complexity of wave behaviors. In the present work, a mathematical model to obtain the solution of the nonlinear wave by coupling the classical Camassa‐Holm equation and the Rosenau‐RLW‐Kawahara equation with the dual term of nonlinearities is proposed. The solution properties are analytically derived. The new model still satisfies the fundamental energy conservative property as the original models. We then apply the energy method to prove the well‐posedness of the model under the solitary wave hypothesis. Some categories of exact solitary wave solutions of the model are described by using the Ansatz method. In addition, we found that the dual term of nonlinearity is essential to obtain the class of analytic solution. Besides, we provide some graphical representations to illustrate the behavior of the traveling wave solutions.

Suggested Citation

  • Nattakorn Sukantamala & Supawan Nanta, 2021. "On Solitary Wave Solutions for the Camassa‐Holm and the Rosenau‐RLW‐Kawahara Equations with the Dual‐Power Law Nonlinearities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlaaa:v:2021:y:2021:i:1:n:6649285
    DOI: 10.1155/2021/6649285
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    References listed on IDEAS

    as
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    4. Abdon Atangana & Necdet Bildik & S. C. Oukouomi Noutchie, 2014. "New Iteration Methods for Time‐Fractional Modified Nonlinear Kawahara Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Xiju Zong & Xingong Cheng & Zhonghua Wang & Zhenlai Han, 2011. "Initial Boundary Value Problem and Asymptotic Stabilization of the Two-Component Camassa-Holm Equation," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-20, September.
    6. Zheng Yin, 2013. "Several Dynamic Properties of Solutions to a Generalized Camassa‐Holm Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Xiumei Lv & Tengwei Shao & Jiacheng Chen, 2013. "The Study of the Solution to a Generalized KdV‐mKdV Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Gang-Wei Wang & Tian-Zhou Xu, 2013. "Group Analysis and New Explicit Solutions of Simplified Modified Kawahara Equation with Variable Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    9. Abdon Atangana & Necdet Bildik & S. C. Oukouomi Noutchie, 2014. "New Iteration Methods for Time-Fractional Modified Nonlinear Kawahara Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, January.
    10. Gang-Wei Wang & Tian-Zhou Xu, 2013. "Group Analysis and New Explicit Solutions of Simplified Modified Kawahara Equation with Variable Coefficients," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, October.
    11. 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.
    12. Xiju Zong & Xingong Cheng & Zhonghua Wang & Zhenlai Han, 2011. "Initial Boundary Value Problem and Asymptotic Stabilization of the Two‐Component Camassa‐Holm Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
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