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Comptes Rendus. Mathématique
Équations différentielles, Systèmes dynamiques
First integrals of the Maxwell–Bloch system
Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 3-11.

Nous étudions les premières intégrales analytiques, rationnelles et C 1 du système de Maxwell–Bloch

E˙=-κE+gP,P˙=-γP+gE,˙=-γ(-0)-4gPE,

κ,γ ,g,γ , 0 sont des paramètres réels. En outre, nous prouvons que ce système est non intégrable rationnel dans le sens de Bogoyavlenskij pour presque toutes les valeurs de paramètres.

We investigate the analytic, rational and C 1 first integrals of the Maxwell–Bloch system

E˙=-κE+gP,P˙=-γP+gE,˙=-γ(-0)-4gPE,

where κ,γ ,g,γ , 0 are real parameters. In addition, we prove this system is rationally non-integrable in the sense of Bogoyavlenskij for almost all parameter values.

Reçu le : 2018-05-17
Révisé le : 2019-12-26
Accepté le : 2020-01-12
Publié le : 2020-03-18
DOI : https://doi.org/10.5802/crmath.6
@article{CRMATH_2020__358_1_3_0,
     author = {Kaiyin Huang and Shaoyun Shi and Wenlei Li},
     title = {First integrals of the Maxwell--Bloch system},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {3--11},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {1},
     year = {2020},
     doi = {10.5802/crmath.6},
     language = {en},
     url = {comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_1_3_0/}
}
Kaiyin Huang; Shaoyun Shi; Wenlei Li. First integrals of the Maxwell–Bloch system. Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 3-11. doi : 10.5802/crmath.6. https://comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_1_3_0/

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