Precise soliton solutions of the Landau-Ginzburg-Higgs equation via the Sardar sub-equation method
Abstract In the realm of nonlinear mathematical physics, the Landau-Ginzburg-Higgs (LGH) equation stands as a pivotal model for understanding complex physical phenomena, including superconductors, phase transitions, and particle interactions. This study applies the Sardar Sub-Equation (SSE) method t...
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| Format: | Article |
| Language: | English |
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Springer
2025-08-01
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| Series: | Discover Applied Sciences |
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| Online Access: | https://doi.org/10.1007/s42452-025-07118-7 |
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| author | Ahmed Refaie Ali Md. Nur Alam Md. Fayz-Al-Asad Mujahid Iqbal Mohammad Hassan |
| author_facet | Ahmed Refaie Ali Md. Nur Alam Md. Fayz-Al-Asad Mujahid Iqbal Mohammad Hassan |
| author_sort | Ahmed Refaie Ali |
| collection | DOAJ |
| description | Abstract In the realm of nonlinear mathematical physics, the Landau-Ginzburg-Higgs (LGH) equation stands as a pivotal model for understanding complex physical phenomena, including superconductors, phase transitions, and particle interactions. This study applies the Sardar Sub-Equation (SSE) method to derive exact soliton solutions for the LGH equation, unveiling diverse wave structures such as kink-shaped, M-shaped, cuspon, and periodic solitons. The computational analysis, carried out using Maple software, provides a robust framework for exploring these nonlinear structures. The results demonstrate the efficiency of the SSE method in obtaining precise analytical solutions, contributing valuable insights into the dynamics of nonlinear wave propagation. These findings have significant implications across various scientific disciplines, including quantum mechanics, material science, and high-energy physics, further establishing the SSE method as an effective tool for solving nonlinear partial differential equations (PDEs). |
| format | Article |
| id | doaj-art-1cb62a28febe466297b1f97c4a04ae88 |
| institution | Kabale University |
| issn | 3004-9261 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Springer |
| record_format | Article |
| series | Discover Applied Sciences |
| spelling | doaj-art-1cb62a28febe466297b1f97c4a04ae882025-08-24T11:45:07ZengSpringerDiscover Applied Sciences3004-92612025-08-017911710.1007/s42452-025-07118-7Precise soliton solutions of the Landau-Ginzburg-Higgs equation via the Sardar sub-equation methodAhmed Refaie Ali0Md. Nur Alam1Md. Fayz-Al-Asad2Mujahid Iqbal3Mohammad Hassan4Department of Mathematics and Computer Science, Faculty of Science, Menoufia UniversityDepartment of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical SciencesDepartment of Mathematics, American International University – BangladeshSchool of Mathematical Sciences, Jiangsu UniversityDepartment of Mathematics and Scientific Computing, Madan Mohan Malaviya University of TechnologyAbstract In the realm of nonlinear mathematical physics, the Landau-Ginzburg-Higgs (LGH) equation stands as a pivotal model for understanding complex physical phenomena, including superconductors, phase transitions, and particle interactions. This study applies the Sardar Sub-Equation (SSE) method to derive exact soliton solutions for the LGH equation, unveiling diverse wave structures such as kink-shaped, M-shaped, cuspon, and periodic solitons. The computational analysis, carried out using Maple software, provides a robust framework for exploring these nonlinear structures. The results demonstrate the efficiency of the SSE method in obtaining precise analytical solutions, contributing valuable insights into the dynamics of nonlinear wave propagation. These findings have significant implications across various scientific disciplines, including quantum mechanics, material science, and high-energy physics, further establishing the SSE method as an effective tool for solving nonlinear partial differential equations (PDEs).https://doi.org/10.1007/s42452-025-07118-7Soliton sagaLandau–Ginzburg–Higgs (LGH) equationSardar Sub-Equation (SSE)Exact soliton solutionsNLPDEsBalance method |
| spellingShingle | Ahmed Refaie Ali Md. Nur Alam Md. Fayz-Al-Asad Mujahid Iqbal Mohammad Hassan Precise soliton solutions of the Landau-Ginzburg-Higgs equation via the Sardar sub-equation method Discover Applied Sciences Soliton saga Landau–Ginzburg–Higgs (LGH) equation Sardar Sub-Equation (SSE) Exact soliton solutions NLPDEs Balance method |
| title | Precise soliton solutions of the Landau-Ginzburg-Higgs equation via the Sardar sub-equation method |
| title_full | Precise soliton solutions of the Landau-Ginzburg-Higgs equation via the Sardar sub-equation method |
| title_fullStr | Precise soliton solutions of the Landau-Ginzburg-Higgs equation via the Sardar sub-equation method |
| title_full_unstemmed | Precise soliton solutions of the Landau-Ginzburg-Higgs equation via the Sardar sub-equation method |
| title_short | Precise soliton solutions of the Landau-Ginzburg-Higgs equation via the Sardar sub-equation method |
| title_sort | precise soliton solutions of the landau ginzburg higgs equation via the sardar sub equation method |
| topic | Soliton saga Landau–Ginzburg–Higgs (LGH) equation Sardar Sub-Equation (SSE) Exact soliton solutions NLPDEs Balance method |
| url | https://doi.org/10.1007/s42452-025-07118-7 |
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