First integrals of the Maxwell–Bloch system
We investigate the analytic, rational and $C^1$ first integrals of the Maxwell–Bloch system \begin{equation*} \dot{E}=-\kappa E+gP,\quad \dot{P}=-\gamma _{\bot }P+gE\triangle , \quad \dot{\triangle }=-\gamma _{\Vert }(\triangle -\triangle _0)-4gPE, \end{equation*} where $\kappa , \gamma _{\bot },...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2020-03-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.6/ |
| _version_ | 1797651567796551680 |
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| author | Huang, Kaiyin Shi, Shaoyun Li, Wenlei |
| author_facet | Huang, Kaiyin Shi, Shaoyun Li, Wenlei |
| author_sort | Huang, Kaiyin |
| collection | DOAJ |
| description | We investigate the analytic, rational and $C^1$ first integrals of the Maxwell–Bloch system
\begin{equation*}
\dot{E}=-\kappa E+gP,\quad \dot{P}=-\gamma _{\bot }P+gE\triangle , \quad \dot{\triangle }=-\gamma _{\Vert }(\triangle -\triangle _0)-4gPE,
\end{equation*}
where $\kappa , \gamma _{\bot }, g, \gamma _{\Vert }, \triangle _0$ are real parameters. In addition, we prove this system is rationally non-integrable in the sense of Bogoyavlenskij for almost all parameter values. |
| first_indexed | 2024-03-11T16:17:42Z |
| format | Article |
| id | doaj.art-d11aa7648d224d9d8546929dcbc6e1fd |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:17:42Z |
| publishDate | 2020-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-d11aa7648d224d9d8546929dcbc6e1fd2023-10-24T14:19:10ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692020-03-01358131110.5802/crmath.610.5802/crmath.6First integrals of the Maxwell–Bloch systemHuang, Kaiyin0https://orcid.org/0000-0003-1905-4642Shi, Shaoyun1Li, Wenlei2School of Mathematics, Jilin University, Changchun 130012, P. R. China; School of Mathematics, Sichuan University, Chengdu 610000, P. R. ChinaSchool of Mathematics, Jilin University, Changchun 130012, P. R. China; State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130012, P. R. ChinaSchool of Mathematics, Jilin University, Changchun 130012, P. R. ChinaWe investigate the analytic, rational and $C^1$ first integrals of the Maxwell–Bloch system \begin{equation*} \dot{E}=-\kappa E+gP,\quad \dot{P}=-\gamma _{\bot }P+gE\triangle , \quad \dot{\triangle }=-\gamma _{\Vert }(\triangle -\triangle _0)-4gPE, \end{equation*} where $\kappa , \gamma _{\bot }, g, \gamma _{\Vert }, \triangle _0$ are real parameters. In addition, we prove this system is rationally non-integrable in the sense of Bogoyavlenskij for almost all parameter values.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.6/ |
| spellingShingle | Huang, Kaiyin Shi, Shaoyun Li, Wenlei First integrals of the Maxwell–Bloch system Comptes Rendus. Mathématique |
| title | First integrals of the Maxwell–Bloch system |
| title_full | First integrals of the Maxwell–Bloch system |
| title_fullStr | First integrals of the Maxwell–Bloch system |
| title_full_unstemmed | First integrals of the Maxwell–Bloch system |
| title_short | First integrals of the Maxwell–Bloch system |
| title_sort | first integrals of the maxwell bloch system |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.6/ |
| work_keys_str_mv | AT huangkaiyin firstintegralsofthemaxwellblochsystem AT shishaoyun firstintegralsofthemaxwellblochsystem AT liwenlei firstintegralsofthemaxwellblochsystem |