Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system
In this paper, we investigate the nonlocal reverse-time Hirota-Maxwell-Bloch system, focusing on its soliton solutions using the Darboux transformation method. By deriving the Darboux transformation for this system, we obtained explicit expressions for the new potentials $ q', p' $, and $...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241666 |
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| author | Zh. Myrzakulova Z. Zakariyeva K. Suleimenov U. Uralbekova K. Yesmakhanova |
| author_facet | Zh. Myrzakulova Z. Zakariyeva K. Suleimenov U. Uralbekova K. Yesmakhanova |
| author_sort | Zh. Myrzakulova |
| collection | DOAJ |
| description | In this paper, we investigate the nonlocal reverse-time Hirota-Maxwell-Bloch system, focusing on its soliton solutions using the Darboux transformation method. By deriving the Darboux transformation for this system, we obtained explicit expressions for the new potentials $ q', p' $, and $ \eta' $ in both the defocusing ($ \kappa = 1 $) and focusing ($ \kappa = -1 $) cases. Our analysis reveals significant differences in soliton behavior depending on the value of $ \kappa $, with the defocusing case producing wide, smooth solitons and the focusing case yielding narrow, highly localized solitons. These results provide a deeper understanding of soliton dynamics in nonlocal integrable systems and lay the groundwork for future studies on the influence of nonlocality in integrable models. |
| format | Article |
| id | doaj-art-821669fc2d78402eb770739861ede6a9 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-821669fc2d78402eb770739861ede6a92025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912350043501510.3934/math.20241666Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch systemZh. Myrzakulova0Z. Zakariyeva1K. Suleimenov2U. Uralbekova3K. Yesmakhanova4Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Kazhymukan, Astana, 010008, KazakhstanFaculty of Physics and Mathematics, M. Utemisov West Kazakhstan University, 162 Nazarbayev, Oral, 090000, KazakhstanFaculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Kazhymukan, Astana, 010008, KazakhstanFaculty of Mechanics and Mathematics, al-Farabi Kazakh National University, 71 al-Farabi, Almaty, 050040, KazakhstanFaculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Kazhymukan, Astana, 010008, KazakhstanIn this paper, we investigate the nonlocal reverse-time Hirota-Maxwell-Bloch system, focusing on its soliton solutions using the Darboux transformation method. By deriving the Darboux transformation for this system, we obtained explicit expressions for the new potentials $ q', p' $, and $ \eta' $ in both the defocusing ($ \kappa = 1 $) and focusing ($ \kappa = -1 $) cases. Our analysis reveals significant differences in soliton behavior depending on the value of $ \kappa $, with the defocusing case producing wide, smooth solitons and the focusing case yielding narrow, highly localized solitons. These results provide a deeper understanding of soliton dynamics in nonlocal integrable systems and lay the groundwork for future studies on the influence of nonlocality in integrable models.https://www.aimspress.com/article/doi/10.3934/math.20241666nonlocal reverse-time hirota and maxwell-bloch systempt-symmetricdarboux transformationexplicit solutionlax pair |
| spellingShingle | Zh. Myrzakulova Z. Zakariyeva K. Suleimenov U. Uralbekova K. Yesmakhanova Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system AIMS Mathematics nonlocal reverse-time hirota and maxwell-bloch system pt-symmetric darboux transformation explicit solution lax pair |
| title | Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system |
| title_full | Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system |
| title_fullStr | Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system |
| title_full_unstemmed | Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system |
| title_short | Explicit solutions of nonlocal reverse-time Hirota-Maxwell-Bloch system |
| title_sort | explicit solutions of nonlocal reverse time hirota maxwell bloch system |
| topic | nonlocal reverse-time hirota and maxwell-bloch system pt-symmetric darboux transformation explicit solution lax pair |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241666 |
| work_keys_str_mv | AT zhmyrzakulova explicitsolutionsofnonlocalreversetimehirotamaxwellblochsystem AT zzakariyeva explicitsolutionsofnonlocalreversetimehirotamaxwellblochsystem AT ksuleimenov explicitsolutionsofnonlocalreversetimehirotamaxwellblochsystem AT uuralbekova explicitsolutionsofnonlocalreversetimehirotamaxwellblochsystem AT kyesmakhanova explicitsolutionsofnonlocalreversetimehirotamaxwellblochsystem |