Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable Coefficient
In this manuscript, we implement analytical multiple soliton wave and singular soliton wave solutions for coupled mKdV with a time-dependent variable coefficient. Based on the similarity transformation and Hirota bilinear technique, we construct both multiple wave kink and wave singular kink solutio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/11/1972 |
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| author | Haroon D. S. Adam Khalid I. A. Ahmed Mukhtar Yagoub Youssif Marin Marin |
| author_facet | Haroon D. S. Adam Khalid I. A. Ahmed Mukhtar Yagoub Youssif Marin Marin |
| author_sort | Haroon D. S. Adam |
| collection | DOAJ |
| description | In this manuscript, we implement analytical multiple soliton wave and singular soliton wave solutions for coupled mKdV with a time-dependent variable coefficient. Based on the similarity transformation and Hirota bilinear technique, we construct both multiple wave kink and wave singular kink solutions for coupled mKdV with a time-dependent variable coefficient. We implement the Hirota bilinear technique to compute analytical solutions for the coupled mKdV system. Such calculations are made by using a software with symbolic computation software, for instance, Maple. Recently some researchers used Maple in order to show that the bilinear method of Hirota is a straightforward technique which can be used in the approach of differential, nonlinear models. We analyzed whether the experiments proved that the procedure is effective and can be successfully used for many other mathematical models used in physics and engineering. The results of this study display that the profiles of multiple-kink and singular-kink soliton types can be efficiently controlled by selecting the particular form of a similar time variable. The changes in the solitons based on the changes in the arbitrary function of time allows for more applications of them in applied sciences. |
| first_indexed | 2024-03-09T16:25:39Z |
| format | Article |
| id | doaj.art-7a9ee6596b3844dc891fa31042a7cf3f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T16:25:39Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7a9ee6596b3844dc891fa31042a7cf3f2023-11-24T15:08:34ZengMDPI AGSymmetry2073-89942023-10-011511197210.3390/sym15111972Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable CoefficientHaroon D. S. Adam0Khalid I. A. Ahmed1Mukhtar Yagoub Youssif2Marin Marin3Department of Basic Sciences, Najran University, P.O. Box 1988, Najran 61441, Saudi ArabiaDepartment of Basic Sciences, Najran University, P.O. Box 1988, Najran 61441, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, RomaniaIn this manuscript, we implement analytical multiple soliton wave and singular soliton wave solutions for coupled mKdV with a time-dependent variable coefficient. Based on the similarity transformation and Hirota bilinear technique, we construct both multiple wave kink and wave singular kink solutions for coupled mKdV with a time-dependent variable coefficient. We implement the Hirota bilinear technique to compute analytical solutions for the coupled mKdV system. Such calculations are made by using a software with symbolic computation software, for instance, Maple. Recently some researchers used Maple in order to show that the bilinear method of Hirota is a straightforward technique which can be used in the approach of differential, nonlinear models. We analyzed whether the experiments proved that the procedure is effective and can be successfully used for many other mathematical models used in physics and engineering. The results of this study display that the profiles of multiple-kink and singular-kink soliton types can be efficiently controlled by selecting the particular form of a similar time variable. The changes in the solitons based on the changes in the arbitrary function of time allows for more applications of them in applied sciences.https://www.mdpi.com/2073-8994/15/11/1972nonlinear modelscoupled mKdVtime-dependent variable coefficientsimilarity transformationHirota bilinear technique |
| spellingShingle | Haroon D. S. Adam Khalid I. A. Ahmed Mukhtar Yagoub Youssif Marin Marin Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable Coefficient Symmetry nonlinear models coupled mKdV time-dependent variable coefficient similarity transformation Hirota bilinear technique |
| title | Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable Coefficient |
| title_full | Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable Coefficient |
| title_fullStr | Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable Coefficient |
| title_full_unstemmed | Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable Coefficient |
| title_short | Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable Coefficient |
| title_sort | multiple soliton solutions for coupled modified korteweg de vries mkdv with a time dependent variable coefficient |
| topic | nonlinear models coupled mKdV time-dependent variable coefficient similarity transformation Hirota bilinear technique |
| url | https://www.mdpi.com/2073-8994/15/11/1972 |
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