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

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...

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Bibliographic Details
Published in:Advances in mathematical physics 2022-07, Vol.2022, p.1-10
Main Authors: Mishra, Shubham, Arora, Geeta, Emadifar, Homan, Sahoo, Soubhagya Kumar, Ghanizadeh, Afshin
Format: Article
Language:English
Subjects:
B spline functions
Basis functions
Canals
Differential equations
Exact solutions
Graphical representations
Korteweg-Devries equation
Nonlinear evolution equations
Norms
Ordinary differential equations
Partial differential equations
Quadratures
Quantum field theory
Solitary waves
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Summary: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.
ISSN:1687-9120
1687-9139
DOI:10.1155/2022/8479433