Stochastic dynamics of symmetry reductions to the parabolic nonlinear model in metamaterials
The Schrödinger model is investigated in this work using electromagnetic pulse waves in metamaterials with parabolic nonlinearity law. The model is first analysed using Lie symmetry analysis to obtain a better grasp of the system's symmetries and invariants. This leads to symmetry reduction, si...
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Elsevier
2025-06-01
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| Series: | Results in Engineering |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590123025017001 |
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| author | Muhammad Idrees Afridi |
| author_facet | Muhammad Idrees Afridi |
| author_sort | Muhammad Idrees Afridi |
| collection | DOAJ |
| description | The Schrödinger model is investigated in this work using electromagnetic pulse waves in metamaterials with parabolic nonlinearity law. The model is first analysed using Lie symmetry analysis to obtain a better grasp of the system's symmetries and invariants. This leads to symmetry reduction, simplifying the problem and facilitating the derivation of soliton solutions. We investigate localised wave packets with stable soliton solutions that maintain their amplitude and form throughout waves. Dark, bright, hyperbolic, and periodic solitons are some of these solutions. Understanding these soliton dynamics is necessary to comprehend the complex behaviour of electromagnetic pulses in metamaterials. Because of their artificial electromagnetic properties, which are not present in nature, metamaterials hold considerable promise for advancements in optics and telecommunications. Finally, to enhance visual comprehension, include density plots and 3-D graphs. This comprehensive approach aids in the elucidation of soliton dynamics in metamaterials and makes it easier to apply these findings in cutting-edge technological fields. |
| format | Article |
| id | doaj-art-e229383ad88740bcaaa1f123a19bfbad |
| institution | OA Journals |
| issn | 2590-1230 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Engineering |
| spelling | doaj-art-e229383ad88740bcaaa1f123a19bfbad2025-08-20T02:35:44ZengElsevierResults in Engineering2590-12302025-06-012610563010.1016/j.rineng.2025.105630Stochastic dynamics of symmetry reductions to the parabolic nonlinear model in metamaterialsMuhammad Idrees Afridi0Research Center for Mathematical Modeling and Simulation, Hanjiang Normal University, Shiyan 442000, China; Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai 602105, Tamil Nadu, India; Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan; Correspondence to: Research Center for Mathematical Modeling and Simulation, Hanjiang Normal University, Shiyan 442000, China.The Schrödinger model is investigated in this work using electromagnetic pulse waves in metamaterials with parabolic nonlinearity law. The model is first analysed using Lie symmetry analysis to obtain a better grasp of the system's symmetries and invariants. This leads to symmetry reduction, simplifying the problem and facilitating the derivation of soliton solutions. We investigate localised wave packets with stable soliton solutions that maintain their amplitude and form throughout waves. Dark, bright, hyperbolic, and periodic solitons are some of these solutions. Understanding these soliton dynamics is necessary to comprehend the complex behaviour of electromagnetic pulses in metamaterials. Because of their artificial electromagnetic properties, which are not present in nature, metamaterials hold considerable promise for advancements in optics and telecommunications. Finally, to enhance visual comprehension, include density plots and 3-D graphs. This comprehensive approach aids in the elucidation of soliton dynamics in metamaterials and makes it easier to apply these findings in cutting-edge technological fields.http://www.sciencedirect.com/science/article/pii/S2590123025017001MetamaterialsSchrödinger modelLie symmetry analysisDynamics of soliton solutions |
| spellingShingle | Muhammad Idrees Afridi Stochastic dynamics of symmetry reductions to the parabolic nonlinear model in metamaterials Results in Engineering Metamaterials Schrödinger model Lie symmetry analysis Dynamics of soliton solutions |
| title | Stochastic dynamics of symmetry reductions to the parabolic nonlinear model in metamaterials |
| title_full | Stochastic dynamics of symmetry reductions to the parabolic nonlinear model in metamaterials |
| title_fullStr | Stochastic dynamics of symmetry reductions to the parabolic nonlinear model in metamaterials |
| title_full_unstemmed | Stochastic dynamics of symmetry reductions to the parabolic nonlinear model in metamaterials |
| title_short | Stochastic dynamics of symmetry reductions to the parabolic nonlinear model in metamaterials |
| title_sort | stochastic dynamics of symmetry reductions to the parabolic nonlinear model in metamaterials |
| topic | Metamaterials Schrödinger model Lie symmetry analysis Dynamics of soliton solutions |
| url | http://www.sciencedirect.com/science/article/pii/S2590123025017001 |
| work_keys_str_mv | AT muhammadidreesafridi stochasticdynamicsofsymmetryreductionstotheparabolicnonlinearmodelinmetamaterials |