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Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg‐de Vries Equation

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  • Shubham Mishra
  • Geeta Arora
  • Homan Emadifar
  • Soubhagya Kumar Sahoo
  • Afshin Ghanizadeh

Abstract

Nonlinear evolution equations are crucial for understanding the phenomena in science and technology. One such equation with periodic solutions that has applications in various fields of physics is the Korteweg‐de Vries (KdV) equation. In the present work, we are concerned with the implementation of a newly defined quintic B‐spline basis function in the differential quadrature method for solving the Korteweg‐de Vries (KdV) equation. The results are presented using four experiments involving a single soliton and the interaction of solitons. The accuracy and efficiency of the method are presented by computing the L2 and L∞ norms along with the conservational quantities in the forms of tables. The results show that the proposed scheme not only gives acceptable results but also consumes less time, as shown by the CPU for the elapsed time in two examples. The graphical representations of the obtained numerical solutions are compared with the exact solution to discuss the nature of solitons and their interactions for more than one soliton.

Suggested Citation

  • Shubham Mishra & Geeta Arora & Homan Emadifar & Soubhagya Kumar Sahoo & Afshin Ghanizadeh, 2022. "Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg‐de Vries Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:8479433
    DOI: 10.1155/2022/8479433
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    References listed on IDEAS

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    1. Kong, Desong & Xu, Yufeng & Zheng, Zhoushun, 2019. "A hybrid numerical method for the KdV equation by finite difference and sinc collocation method," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 61-72.
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