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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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/8479433 |
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| author | Shubham Mishra Geeta Arora Homan Emadifar Soubhagya Kumar Sahoo Afshin Ghanizadeh |
| author_facet | Shubham Mishra Geeta Arora Homan Emadifar Soubhagya Kumar Sahoo Afshin Ghanizadeh |
| author_sort | Shubham Mishra |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e54d63a58f2043c193b9077fb3bae22c |
| institution | OA Journals |
| issn | 1687-9139 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-e54d63a58f2043c193b9077fb3bae22c2025-08-20T02:21:19ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/8479433Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg-de Vries EquationShubham Mishra0Geeta Arora1Homan Emadifar2Soubhagya Kumar Sahoo3Afshin Ghanizadeh4Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of StatisticsNonlinear 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.http://dx.doi.org/10.1155/2022/8479433 |
| spellingShingle | Shubham Mishra Geeta Arora Homan Emadifar Soubhagya Kumar Sahoo Afshin Ghanizadeh Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg-de Vries Equation Advances in Mathematical Physics |
| title | Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg-de Vries Equation |
| title_full | Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg-de Vries Equation |
| title_fullStr | Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg-de Vries Equation |
| title_full_unstemmed | Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg-de Vries Equation |
| title_short | Differential Quadrature Method to Examine the Dynamical Behavior of Soliton Solutions to the Korteweg-de Vries Equation |
| title_sort | differential quadrature method to examine the dynamical behavior of soliton solutions to the korteweg de vries equation |
| url | http://dx.doi.org/10.1155/2022/8479433 |
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