Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns
The aim of current work is to establish novel traveling wave solutions of the nonlinear Atangana conformable Klein - Gordon equation using a new extended direct algebraic technique. The Klein - Gordon equation is the relativistic state of the Schrödinger equation with a second - order time derivativ...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003218 |
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| author | Hadi Rezazadeh Mohammad Ali Hosseinzadeh Lahib Ibrahim Zaidan Fatima SD. Awad Fiza Batool Soheil Salahshour |
| author_facet | Hadi Rezazadeh Mohammad Ali Hosseinzadeh Lahib Ibrahim Zaidan Fatima SD. Awad Fiza Batool Soheil Salahshour |
| author_sort | Hadi Rezazadeh |
| collection | DOAJ |
| description | The aim of current work is to establish novel traveling wave solutions of the nonlinear Atangana conformable Klein - Gordon equation using a new extended direct algebraic technique. The Klein - Gordon equation is the relativistic state of the Schrödinger equation with a second - order time derivative and zero spin. Complex wave variable transformation is used to convert Atangana conformable nonlinear differential equation into an ordinary differential equation. Using the proposed technique based on Maple software structure, various types of solutions, such as, generalized trigonometric, generalized hyperbolic, and exponential functions, are established. When special parameteric values are considered for this method, solitary wave solutions can be obtained through other methods, such as the (G′G)-expansion method, the modified Kudryashov method, the sub-equation method, and so forth. A physical explanation is provided for the solutions under consideration to enhance comprehension of the physical phenomena resulting from the obtained solutions, provided that the physical parameters are set appropriately using 3D, 2D, and contour simulations. The results demonstrated that the new extended direct algebraic method provides a more potent mathematical tool for solving numerous more nonlinear partial differential equations with the aid of symbolic computation. |
| format | Article |
| id | doaj-art-1ab0d84b7ad84f54a1792334345109ef |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-1ab0d84b7ad84f54a1792334345109ef2024-12-13T11:05:37ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-0112100935Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patternsHadi Rezazadeh0Mohammad Ali Hosseinzadeh1Lahib Ibrahim Zaidan2Fatima SD. Awad3Fiza Batool4Soheil Salahshour5Faculty of Engineering Modern Technologies, Amol University of Special Modern Technologies, Amol, Iran; Corresponding author.Faculty of Engineering Modern Technologies, Amol University of Special Modern Technologies, Amol, IranEducation College, University of Babylon, Babil, IraqDepartment of Mathematics, College of Education for Pure Sciences, University of Kerbela, IraqSchool of Mathematics, Minhaj University Lahore 54590, PakistanFaculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey; Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey; Department of Computer Science and Mathematics, Lebanese American University, Beirut, LebanonThe aim of current work is to establish novel traveling wave solutions of the nonlinear Atangana conformable Klein - Gordon equation using a new extended direct algebraic technique. The Klein - Gordon equation is the relativistic state of the Schrödinger equation with a second - order time derivative and zero spin. Complex wave variable transformation is used to convert Atangana conformable nonlinear differential equation into an ordinary differential equation. Using the proposed technique based on Maple software structure, various types of solutions, such as, generalized trigonometric, generalized hyperbolic, and exponential functions, are established. When special parameteric values are considered for this method, solitary wave solutions can be obtained through other methods, such as the (G′G)-expansion method, the modified Kudryashov method, the sub-equation method, and so forth. A physical explanation is provided for the solutions under consideration to enhance comprehension of the physical phenomena resulting from the obtained solutions, provided that the physical parameters are set appropriately using 3D, 2D, and contour simulations. The results demonstrated that the new extended direct algebraic method provides a more potent mathematical tool for solving numerous more nonlinear partial differential equations with the aid of symbolic computation.http://www.sciencedirect.com/science/article/pii/S2666818124003218Traveling wave solutionNew extended direct algebraic techniqueAtangana conformable derivativeNonlinear Klein-Gordon equation |
| spellingShingle | Hadi Rezazadeh Mohammad Ali Hosseinzadeh Lahib Ibrahim Zaidan Fatima SD. Awad Fiza Batool Soheil Salahshour Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns Partial Differential Equations in Applied Mathematics Traveling wave solution New extended direct algebraic technique Atangana conformable derivative Nonlinear Klein-Gordon equation |
| title | Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns |
| title_full | Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns |
| title_fullStr | Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns |
| title_full_unstemmed | Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns |
| title_short | Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns |
| title_sort | innovative approache for the nonlinear atangana conformable klein gordon equation unveiling traveling wave patterns |
| topic | Traveling wave solution New extended direct algebraic technique Atangana conformable derivative Nonlinear Klein-Gordon equation |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003218 |
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