[Sur les réalisations Hamilton–Poisson des déformations intégrables des équations de Maxwell–Bloch]
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.
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@article{CRMATH_2017__355_5_596_0,
author = {L\u{a}zureanu, Cristian},
title = {On the {Hamilton{\textendash}Poisson} realizations of the integrable deformations of the {Maxwell{\textendash}Bloch} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {596--600},
publisher = {Elsevier},
volume = {355},
number = {5},
year = {2017},
doi = {10.1016/j.crma.2017.04.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.04.002/}
}
TY - JOUR AU - Lăzureanu, Cristian TI - On the Hamilton–Poisson realizations of the integrable deformations of the Maxwell–Bloch equations JO - Comptes Rendus. Mathématique PY - 2017 SP - 596 EP - 600 VL - 355 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.04.002/ DO - 10.1016/j.crma.2017.04.002 LA - en ID - CRMATH_2017__355_5_596_0 ER -
%0 Journal Article %A Lăzureanu, Cristian %T On the Hamilton–Poisson realizations of the integrable deformations of the Maxwell–Bloch equations %J Comptes Rendus. Mathématique %D 2017 %P 596-600 %V 355 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.04.002/ %R 10.1016/j.crma.2017.04.002 %G en %F CRMATH_2017__355_5_596_0
Lăzureanu, Cristian. On the Hamilton–Poisson realizations of the integrable deformations of the Maxwell–Bloch equations. Comptes Rendus. Mathématique, Tome 355 (2017) no. 5, pp. 596-600. doi : 10.1016/j.crma.2017.04.002. http://www.numdam.org/articles/10.1016/j.crma.2017.04.002/
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