Comptes Rendus
no. 1
Équations différentielles, Systèmes dynamiques
First integrals of the Maxwell–Bloch system
Kaiyin Huang1, 2  ; Shaoyun Shi1, 3 ; Wenlei Li1
1 School of Mathematics, Jilin University, Changchun 130012, P. R. China
2 School of Mathematics, Sichuan University, Chengdu 610000, P. R. China
3 State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130012, P. R. China
Comptes Rendus. Mathématique, Volume 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 ˙=-γ ⊥ P+gE▵,▵ ˙=-γ ∥ (▵-▵ 0 )-4gPE,

où 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 ˙=-γ ⊥ P+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.

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DOI : 10.5802/crmath.6
Kaiyin Huang 1, 2 ; Shaoyun Shi 1, 3 ; Wenlei Li 1

1 School of Mathematics, Jilin University, Changchun 130012, P. R. China
2 School of Mathematics, Sichuan University, Chengdu 610000, P. R. China
3 State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130012, P. R. China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {First integrals of the {Maxwell{\textendash}Bloch} system},
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     pages = {3--11},
     publisher = {Acad\'emie des sciences, Paris},
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     language = {en},
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Kaiyin Huang; Shaoyun Shi; Wenlei Li. First integrals of the Maxwell–Bloch system. Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 3-11. doi : 10.5802/crmath.6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.6/

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