Comptes Rendus
no. 5
Dynamical systems
On the Hamilton–Poisson realizations of the integrable deformations of the Maxwell–Bloch equations
[Sur les réalisations Hamilton–Poisson des déformations intégrables des équations de Maxwell–Bloch]

Présenté par : Claire Voisin

Cristian Lăzureanu1
1 Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei nr. 2, Timişoara, 300006, Romania
Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 596-600.

Dans cette Note, nous construisons des déformations intégrables des équations de Maxwell–Bloch en modifiant leurs constantes de mouvement. Nous obtenons deux réalisations Hamilton–Poisson du nouveau système. De plus, nous prouvons que le système obtenu admet des réalisations Hamilton–Poisson infiniment nombreuses. Nous présentons une approche Hamilton–Poisson du système obtenu en considérant deux fonctions particulières de déformation.

In this note, we construct integrable deformations of the three-dimensional real valued Maxwell–Bloch equations by modifying their constants of motions. We obtain two Hamilton–Poisson realizations of the new system. Moreover, we prove that the obtained system has infinitely many Hamilton–Poisson realizations. Particularly, we present a Hamilton–Poisson approach of the system obtained considering two concrete deformation functions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.04.002
Cristian Lăzureanu 1

1 Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei nr. 2, Timişoara, 300006, Romania 
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Cristian Lăzureanu. On the Hamilton–Poisson realizations of the integrable deformations of the Maxwell–Bloch equations. Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 596-600. doi : 10.1016/j.crma.2017.04.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.04.002/

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