Lie group classification and conservation laws of a (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation
In this article, the (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation is studied using the classical Lie symmetry method. A complete Lie group classification is conducted to derive the specific forms of the arbitrary smooth functions included in the equation, resulting in two distinct c...
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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/S2666818124003486 |
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| author | Faiza Arif Adil Jhangeer F.M. Mahomed F.D. Zaman |
| author_facet | Faiza Arif Adil Jhangeer F.M. Mahomed F.D. Zaman |
| author_sort | Faiza Arif |
| collection | DOAJ |
| description | In this article, the (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation is studied using the classical Lie symmetry method. A complete Lie group classification is conducted to derive the specific forms of the arbitrary smooth functions included in the equation, resulting in two distinct cases. Using the similarity transformation method, the reductions of the considered equation in the form of ordinary differential equations are obtained. Several invariant solutions including the traveling wave solutions and soliton solutions of the (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation are uncovered. Also, the results are represented through 2D and 3D graphs with their physical interpretations. Notably, using the partial Lagrangian method, the conservation laws are derived, which also yield two separate cases with several subcases. These results offer better insights into the solution properties of nonlinear damped Klein–Gordon Fock equation and other complex nonlinear wave equations. |
| format | Article |
| id | doaj-art-6d38d822a3d848c0ae6ff497e2d05f88 |
| 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-6d38d822a3d848c0ae6ff497e2d05f882024-12-13T11:05:45ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-0112100962Lie group classification and conservation laws of a (2+1)-dimensional nonlinear damped Klein–Gordon Fock equationFaiza Arif0Adil Jhangeer1F.M. Mahomed2F.D. Zaman3Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanIT4Innovations, VSB-Technical University of Ostrava, Ostrava-Poruba, Czech Republic; Department of Mathematics, Namal University, Talagang Road, Mianwali 42250, Pakistan; Corresponding author at: IT4Innovations, VSB-Technical University of Ostrava, Ostrava-Poruba, Czech Republic.DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South AfricaAbdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanIn this article, the (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation is studied using the classical Lie symmetry method. A complete Lie group classification is conducted to derive the specific forms of the arbitrary smooth functions included in the equation, resulting in two distinct cases. Using the similarity transformation method, the reductions of the considered equation in the form of ordinary differential equations are obtained. Several invariant solutions including the traveling wave solutions and soliton solutions of the (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation are uncovered. Also, the results are represented through 2D and 3D graphs with their physical interpretations. Notably, using the partial Lagrangian method, the conservation laws are derived, which also yield two separate cases with several subcases. These results offer better insights into the solution properties of nonlinear damped Klein–Gordon Fock equation and other complex nonlinear wave equations.http://www.sciencedirect.com/science/article/pii/S2666818124003486Mathematical modelLie symmetry analysisEquivalence transformationsReductionsTraveling wave solutionsPartial Lagrangian approach |
| spellingShingle | Faiza Arif Adil Jhangeer F.M. Mahomed F.D. Zaman Lie group classification and conservation laws of a (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation Partial Differential Equations in Applied Mathematics Mathematical model Lie symmetry analysis Equivalence transformations Reductions Traveling wave solutions Partial Lagrangian approach |
| title | Lie group classification and conservation laws of a (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation |
| title_full | Lie group classification and conservation laws of a (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation |
| title_fullStr | Lie group classification and conservation laws of a (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation |
| title_full_unstemmed | Lie group classification and conservation laws of a (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation |
| title_short | Lie group classification and conservation laws of a (2+1)-dimensional nonlinear damped Klein–Gordon Fock equation |
| title_sort | lie group classification and conservation laws of a 2 1 dimensional nonlinear damped klein gordon fock equation |
| topic | Mathematical model Lie symmetry analysis Equivalence transformations Reductions Traveling wave solutions Partial Lagrangian approach |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003486 |
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