# 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} }

## 16 Citations

### Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System

- Mathematics
- 2017

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.…

### On the Integrable Deformations of the Maximally Superintegrable Systems

- MathematicsSymmetry
- 2021

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.

### On the integrable deformations of a system related to the motion of two vortices in an ideal incompressible fluid

- MathematicsITM 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…

### Stability and Energy-Casimir Mapping for Integrable Deformations of the Kermack-McKendrick System

- MathematicsAdvances in Mathematical Physics
- 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…

### On a deformed version of the T system

- 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…

### Integrable Deformations of Three-Dimensional Chaotic Systems

- MathematicsInt. J. Bifurc. Chaos
- 2018

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 ...

### Integrable Deformations and Dynamical Properties of Systems with Constant Population

- MathematicsMathematics
- 2021

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…

### Integrable deformations, bi-Hamiltonian structures and nonintegrability of a generalized Rikitake system

- MathematicsInternational 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…

### On the dynamics of a Hamilton-Poisson system

- 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.…

### Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method

- MathematicsMathematics
- 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…

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In this paper a system derived by an optimal control problem for the ball-plate dynamics is considered. Symplectic and Lagrangian realizations are given and some symmetries are studied. The image of…

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