A Variety of New Traveling Wave Packets and Conservation Laws to the Nonlinear Low-Pass Electrical Transmission Lines via Lie Analysis
This research is based on computing the new wave packets and conserved quantities to the nonlinear low-pass electrical transmission lines (NLETLs) via the group-theoretic method. By using the group-theoretic technique, we analyse the NLETLs and compute infinitesimal generators. The resulting equatio...
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MDPI AG
2021-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/170 |
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| author | Muhammad Bilal Riaz Jan Awrejcewicz Adil Jhangeer Muhammad Junaid-U-Rehman |
| author_facet | Muhammad Bilal Riaz Jan Awrejcewicz Adil Jhangeer Muhammad Junaid-U-Rehman |
| author_sort | Muhammad Bilal Riaz |
| collection | DOAJ |
| description | This research is based on computing the new wave packets and conserved quantities to the nonlinear low-pass electrical transmission lines (NLETLs) via the group-theoretic method. By using the group-theoretic technique, we analyse the NLETLs and compute infinitesimal generators. The resulting equations concede two-dimensional Lie algebra. Then, we have to find the commutation relation of the entire vector field and observe that the obtained generators make an abelian algebra. The optimal system is computed by using the entire vector field and using the concept of abelian algebra. With the help of an optimal system, NLETLs convert into nonlinear ODE. The modified Khater method (MKM) is used to find the wave packets by using the resulting ODEs for a supposed model. To represent the physical importance of the considered model, some <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mi>D</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>D</mi></mrow></semantics></math></inline-formula>, and density diagrams of acquired results are plotted by using Mathematica under the suitable choice of involving parameter values. Furthermore, all derived results were verified by putting them back into the assumed equation with the aid of Maple software. Further, the conservation laws of NLETLs are computed by the multiplier method. |
| first_indexed | 2024-03-10T04:05:07Z |
| format | Article |
| id | doaj.art-3057fb0ea1564c05bc9c9b3b86648043 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:07Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-3057fb0ea1564c05bc9c9b3b866480432023-11-23T08:23:13ZengMDPI AGFractal and Fractional2504-31102021-10-015417010.3390/fractalfract5040170A Variety of New Traveling Wave Packets and Conservation Laws to the Nonlinear Low-Pass Electrical Transmission Lines via Lie AnalysisMuhammad Bilal Riaz0Jan Awrejcewicz1Adil Jhangeer2Muhammad Junaid-U-Rehman3Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, PolandDepartment of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, PolandDepartment of Mathematics, Namal University, Talagang Road, Mianwali 42250, PakistanDepartment of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, PakistanThis research is based on computing the new wave packets and conserved quantities to the nonlinear low-pass electrical transmission lines (NLETLs) via the group-theoretic method. By using the group-theoretic technique, we analyse the NLETLs and compute infinitesimal generators. The resulting equations concede two-dimensional Lie algebra. Then, we have to find the commutation relation of the entire vector field and observe that the obtained generators make an abelian algebra. The optimal system is computed by using the entire vector field and using the concept of abelian algebra. With the help of an optimal system, NLETLs convert into nonlinear ODE. The modified Khater method (MKM) is used to find the wave packets by using the resulting ODEs for a supposed model. To represent the physical importance of the considered model, some <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mi>D</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>D</mi></mrow></semantics></math></inline-formula>, and density diagrams of acquired results are plotted by using Mathematica under the suitable choice of involving parameter values. Furthermore, all derived results were verified by putting them back into the assumed equation with the aid of Maple software. Further, the conservation laws of NLETLs are computed by the multiplier method.https://www.mdpi.com/2504-3110/5/4/170nonlinear low-pass electrical transmission linesmodified khater methodmultiplier approachlie analysistravelling wave patternsconservation laws |
| spellingShingle | Muhammad Bilal Riaz Jan Awrejcewicz Adil Jhangeer Muhammad Junaid-U-Rehman A Variety of New Traveling Wave Packets and Conservation Laws to the Nonlinear Low-Pass Electrical Transmission Lines via Lie Analysis Fractal and Fractional nonlinear low-pass electrical transmission lines modified khater method multiplier approach lie analysis travelling wave patterns conservation laws |
| title | A Variety of New Traveling Wave Packets and Conservation Laws to the Nonlinear Low-Pass Electrical Transmission Lines via Lie Analysis |
| title_full | A Variety of New Traveling Wave Packets and Conservation Laws to the Nonlinear Low-Pass Electrical Transmission Lines via Lie Analysis |
| title_fullStr | A Variety of New Traveling Wave Packets and Conservation Laws to the Nonlinear Low-Pass Electrical Transmission Lines via Lie Analysis |
| title_full_unstemmed | A Variety of New Traveling Wave Packets and Conservation Laws to the Nonlinear Low-Pass Electrical Transmission Lines via Lie Analysis |
| title_short | A Variety of New Traveling Wave Packets and Conservation Laws to the Nonlinear Low-Pass Electrical Transmission Lines via Lie Analysis |
| title_sort | variety of new traveling wave packets and conservation laws to the nonlinear low pass electrical transmission lines via lie analysis |
| topic | nonlinear low-pass electrical transmission lines modified khater method multiplier approach lie analysis travelling wave patterns conservation laws |
| url | https://www.mdpi.com/2504-3110/5/4/170 |
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