# On the Hamilton–Poisson realizations of the integrable deformations of the Maxwell–Bloch equations

```@article{Lzureanu2017OnTH,
title={On the Hamilton–Poisson realizations of the integrable deformations of the Maxwell–Bloch equations},
author={Cristian Lăzureanu},
journal={Comptes Rendus Mathematique},
year={2017},
volume={355},
pages={596-600}
}```
• C. Lăzureanu
• Published 1 May 2017
• Mathematics
• Comptes Rendus Mathematique
16 Citations
Integrable deformations of an integrable case of the Rikitake system are constructed by modifying its constants of motions. Hamilton-Poisson realizations of these integrable deformations are given.
This paper alters the constants of motion, and using these new functions, construct a new system which is an integrable deformation of the initial system, and new maximally superintegrable systems are obtained.
• Mathematics
ITM Web of Conferences
• 2019
Altering the first integrals of an integrable system integrable deformations of the given system are obtained. These integrable deformations are also integrable systems, and they generalize the
• Mathematics
• 2018
Integrable deformations of a Hamilton-Poisson system can be obtained altering its constants of motion. These deformations are integrable systems that can have various dynamical properties. In this
• Mathematics
• 2019
We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation
The integrable deformation method for a three-dimensional Hamilton–Poisson system consists in alteration of its constants of motion in order to obtain a new Hamilton–Poisson system. We assume that ...
In this paper we consider systems of three autonomous first-order differential equations x˙=f(x),x=(x,y,z),f=(f1,f2,f3) such that x(t)+y(t)+z(t) is constant for all t. We present some
• Mathematics
International Journal of Geometric Methods in Modern Physics
• 2019
The aim of this paper is to investigate a generalized Rikitake system from the integrability point of view. For the integrable case, we derive a family of integrable deformations of the generalized
• Mathematics
• 2019
The dynamics of a three-dimensional Hamilton-Poisson system is closely related to its constants of motion, the energy or Hamiltonian function \$H\$ and a Casimir \$C\$ of the corresponding Lie algebra.
• Mathematics
Mathematics
• 2022
This paper emphasizes some geometrical properties of the Maxwell–Bloch equations. Based on these properties, the closed-form solutions of their equations are established. Thus, the Maxwell–Bloch