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 },...
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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/ |
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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 |