Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods
The Schamel-Korteweg-de Vries (S-KdV) equation including a square root nonlinearity is very important pattern for the research of ion-acoustic waves in plasma and dusty plasma. As known, it is significant to discover the traveling wave solutions of such equations. Therefore, in this paper, some new...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2023-07-01
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| Series: | Universal Journal of Mathematics and Applications |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/3102437 |
| _version_ | 1827381409093779456 |
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| author | Seydi Battal Gazi Karakoç Mona Mehanna Khalid K. Ali |
| author_facet | Seydi Battal Gazi Karakoç Mona Mehanna Khalid K. Ali |
| author_sort | Seydi Battal Gazi Karakoç |
| collection | DOAJ |
| description | The Schamel-Korteweg-de Vries (S-KdV) equation including a square root nonlinearity is very important pattern for the research of ion-acoustic waves in plasma and dusty plasma. As known, it is significant to discover the traveling wave solutions of such equations. Therefore, in this paper, some new traveling wave solutions of the S-KdV equation, which arises in plasma physics in the study of ion acoustic solitons when electron trapping is present and also it governs the electrostatic potential for a certain electron distribution in velocity space, are constructed. For this purpose, the Bernoulli Sub-ODE and modified auxiliary equation methods are used. It has been shown that the suggested methods are effective and give different types of function solutions as: hyperbolic, trigonometric, power,
exponential, and rational functions. The applied computational strategies are direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The results found in the paper are of great interest and may also be used to discover the wave sorts and
specialities in several plasma systems. |
| first_indexed | 2024-03-08T13:55:48Z |
| format | Article |
| id | doaj.art-0e257928e40a4a3abbcc98d0f8e77b93 |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T13:55:48Z |
| publishDate | 2023-07-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-0e257928e40a4a3abbcc98d0f8e77b932024-01-15T15:13:18ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532023-07-0162657510.32323/ujma.12875241225Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different MethodsSeydi Battal Gazi Karakoç0Mona Mehanna1Khalid K. Ali2Nevşehir Hacı Bektaş Veli UniversityMTI UniversityAL-Azhar UniversityThe Schamel-Korteweg-de Vries (S-KdV) equation including a square root nonlinearity is very important pattern for the research of ion-acoustic waves in plasma and dusty plasma. As known, it is significant to discover the traveling wave solutions of such equations. Therefore, in this paper, some new traveling wave solutions of the S-KdV equation, which arises in plasma physics in the study of ion acoustic solitons when electron trapping is present and also it governs the electrostatic potential for a certain electron distribution in velocity space, are constructed. For this purpose, the Bernoulli Sub-ODE and modified auxiliary equation methods are used. It has been shown that the suggested methods are effective and give different types of function solutions as: hyperbolic, trigonometric, power, exponential, and rational functions. The applied computational strategies are direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The results found in the paper are of great interest and may also be used to discover the wave sorts and specialities in several plasma systems.https://dergipark.org.tr/tr/download/article-file/3102437auxiliary equation methodbernoulli sub-ode methodmodifiedschamel--korteweg--de vries equationtravelling wave solutions |
| spellingShingle | Seydi Battal Gazi Karakoç Mona Mehanna Khalid K. Ali Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods Universal Journal of Mathematics and Applications auxiliary equation method bernoulli sub-ode method modified schamel--korteweg--de vries equation travelling wave solutions |
| title | Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods |
| title_full | Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods |
| title_fullStr | Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods |
| title_full_unstemmed | Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods |
| title_short | Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods |
| title_sort | exact traveling wave solutions of the schamel kdv equation with two different methods |
| topic | auxiliary equation method bernoulli sub-ode method modified schamel--korteweg--de vries equation travelling wave solutions |
| url | https://dergipark.org.tr/tr/download/article-file/3102437 |
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