Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation
The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. This paper presents the analysis of the approximate symmetries along with conservation laws corresponding to the perturbed KdV equation for di...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/7710333 |
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| _version_ | 1832560524806586368 |
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| author | Tahir Ayaz Farhad Ali Wali Khan Mashwani Israr Ali Khan Zabidin Salleh Ikramullah |
| author_facet | Tahir Ayaz Farhad Ali Wali Khan Mashwani Israr Ali Khan Zabidin Salleh Ikramullah |
| author_sort | Tahir Ayaz |
| collection | DOAJ |
| description | The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. This paper presents the analysis of the approximate symmetries along with conservation laws corresponding to the perturbed KdV equation for different classes of the perturbed function. Partial Lagrange method is used to obtain the approximate symmetries and their corresponding conservation laws of the KdV equation. The purpose of this study is to find particular perturbation (function) for which the number of approximate symmetries of perturbed KdV equation is greater than the number of symmetries of KdV equation so that explore something hidden in the system. |
| format | Article |
| id | doaj-art-6b03baae7e4f4dc4995e762a7f40d4bc |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6b03baae7e4f4dc4995e762a7f40d4bc2025-02-03T01:27:21ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/77103337710333Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries EquationTahir Ayaz0Farhad Ali1Wali Khan Mashwani2Israr Ali Khan3Zabidin Salleh4Ikramullah5Institute of Numerical Sciences, Kohat University of Science& Technology, Kohat, PakistanInstitute of Numerical Sciences, Kohat University of Science& Technology, Kohat, PakistanInstitute of Numerical Sciences, Kohat University of Science& Technology, Kohat, PakistanInstitute of Numerical Sciences, Kohat University of Science& Technology, Kohat, PakistanDepartment of Mathematics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, MalaysiaDepartment of Physics, Kohat University of Science& Technology, Kohat, PakistanThe Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. This paper presents the analysis of the approximate symmetries along with conservation laws corresponding to the perturbed KdV equation for different classes of the perturbed function. Partial Lagrange method is used to obtain the approximate symmetries and their corresponding conservation laws of the KdV equation. The purpose of this study is to find particular perturbation (function) for which the number of approximate symmetries of perturbed KdV equation is greater than the number of symmetries of KdV equation so that explore something hidden in the system.http://dx.doi.org/10.1155/2021/7710333 |
| spellingShingle | Tahir Ayaz Farhad Ali Wali Khan Mashwani Israr Ali Khan Zabidin Salleh Ikramullah Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation Journal of Mathematics |
| title | Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation |
| title_full | Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation |
| title_fullStr | Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation |
| title_full_unstemmed | Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation |
| title_short | Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation |
| title_sort | approximate symmetries analysis and conservation laws corresponding to perturbed korteweg de vries equation |
| url | http://dx.doi.org/10.1155/2021/7710333 |
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