Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913454732869632 |
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| author | Biondini, Gino Prinari, Barbara Zhang, Zechuan |
| author_facet | Biondini, Gino Prinari, Barbara Zhang, Zechuan |
| contents | The Maxwell-Bloch system of equations with inhomogeneous broadening is studied, and the local and global well-posedness of the corresponding initial-boundary value problem is established by taking advantage of the integrability of the system and making use of the corresponding inverse scattering transform. A key ingredient in the analysis is the $L^2$-Sobolev bijectivity of the direct and inverse scattering transform established by Xin Zhou for the focusing Zakharov-Shabat problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19770 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening Biondini, Gino Prinari, Barbara Zhang, Zechuan Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs The Maxwell-Bloch system of equations with inhomogeneous broadening is studied, and the local and global well-posedness of the corresponding initial-boundary value problem is established by taking advantage of the integrability of the system and making use of the corresponding inverse scattering transform. A key ingredient in the analysis is the $L^2$-Sobolev bijectivity of the direct and inverse scattering transform established by Xin Zhou for the focusing Zakharov-Shabat problem. |
| title | Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2407.19770 |