Ordinary Differential Equations, Dynamical Systems
First integrals of the Maxwell–Bloch system
Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 3-11.

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.

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,

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.

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

1 School of Mathematics, Sichuan University, Chengdu 610000, P. R. China
2 School of Mathematics, Jilin University, Changchun 130012, P. R. China
3 State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130012, P. R. China
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Huang, Kaiyin; Shi, Shaoyun; Li, Wenlei. First integrals of the Maxwell–Bloch system. Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 3-11. doi : 10.5802/crmath.6. http://archive.numdam.org/articles/10.5802/crmath.6/

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