Soliton Solutions of Klein–Fock–Gordon Equation Using Sardar Subequation Method
The Klein–Fock–Gordon equation (KFGE), defined as the equation of relativistic wave related to NLEEs, has numerous implications for energy particle physics and is useful as a model for several types of matter, with deviation in the basic stuffs of particles and in crystals. In this work, the Sardar...
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3377 |
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| author | Hamood Ur Rehman Ifrah Iqbal Suhad Subhi Aiadi Nabil Mlaiki Muhammad Shoaib Saleem |
| author_facet | Hamood Ur Rehman Ifrah Iqbal Suhad Subhi Aiadi Nabil Mlaiki Muhammad Shoaib Saleem |
| author_sort | Hamood Ur Rehman |
| collection | DOAJ |
| description | The Klein–Fock–Gordon equation (KFGE), defined as the equation of relativistic wave related to NLEEs, has numerous implications for energy particle physics and is useful as a model for several types of matter, with deviation in the basic stuffs of particles and in crystals. In this work, the Sardar subequation method (SSM) is used for finding the solution of this KFGE. The advantage of SSM is that it provides many different kinds of solitons, such as dark, bright, singular, periodic singular, combined dark–singular and combined dark–bright solitons. The results show that the SSM is very reliable, simple and can be functionalized to other nonlinear equations. It is verified that all the attained solutions are stable by modulation instability process. To enhance the physical description of solutions, some 3D, contour and 2D graphs are plotted by taking precise values of parameters using Maple 18. |
| first_indexed | 2024-03-09T23:15:01Z |
| format | Article |
| id | doaj.art-bae2ba22d4254a4abbe1478ffe846fea |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:01Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-bae2ba22d4254a4abbe1478ffe846fea2023-11-23T17:37:43ZengMDPI AGMathematics2227-73902022-09-011018337710.3390/math10183377Soliton Solutions of Klein–Fock–Gordon Equation Using Sardar Subequation MethodHamood Ur Rehman0Ifrah Iqbal1Suhad Subhi Aiadi2Nabil Mlaiki3Muhammad Shoaib Saleem4Department of Mathematics, University of Okara, Okara 56300, PakistanDepartment of Mathematics, University of Okara, Okara 56300, PakistanDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics, University of Okara, Okara 56300, PakistanThe Klein–Fock–Gordon equation (KFGE), defined as the equation of relativistic wave related to NLEEs, has numerous implications for energy particle physics and is useful as a model for several types of matter, with deviation in the basic stuffs of particles and in crystals. In this work, the Sardar subequation method (SSM) is used for finding the solution of this KFGE. The advantage of SSM is that it provides many different kinds of solitons, such as dark, bright, singular, periodic singular, combined dark–singular and combined dark–bright solitons. The results show that the SSM is very reliable, simple and can be functionalized to other nonlinear equations. It is verified that all the attained solutions are stable by modulation instability process. To enhance the physical description of solutions, some 3D, contour and 2D graphs are plotted by taking precise values of parameters using Maple 18.https://www.mdpi.com/2227-7390/10/18/3377Klein–Fock–Gordon equation (KFGE)Sardar subequation method (SSM)non-linear evolution equations (NLEEs)stability analysis |
| spellingShingle | Hamood Ur Rehman Ifrah Iqbal Suhad Subhi Aiadi Nabil Mlaiki Muhammad Shoaib Saleem Soliton Solutions of Klein–Fock–Gordon Equation Using Sardar Subequation Method Mathematics Klein–Fock–Gordon equation (KFGE) Sardar subequation method (SSM) non-linear evolution equations (NLEEs) stability analysis |
| title | Soliton Solutions of Klein–Fock–Gordon Equation Using Sardar Subequation Method |
| title_full | Soliton Solutions of Klein–Fock–Gordon Equation Using Sardar Subequation Method |
| title_fullStr | Soliton Solutions of Klein–Fock–Gordon Equation Using Sardar Subequation Method |
| title_full_unstemmed | Soliton Solutions of Klein–Fock–Gordon Equation Using Sardar Subequation Method |
| title_short | Soliton Solutions of Klein–Fock–Gordon Equation Using Sardar Subequation Method |
| title_sort | soliton solutions of klein fock gordon equation using sardar subequation method |
| topic | Klein–Fock–Gordon equation (KFGE) Sardar subequation method (SSM) non-linear evolution equations (NLEEs) stability analysis |
| url | https://www.mdpi.com/2227-7390/10/18/3377 |
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