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
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16 Citations
Background Citations
2
Methods Citations
2
Results Citations
1

16 Citations

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

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Integrable Deformations of Three-Dimensional Chaotic Systems

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 ...

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

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

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

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…

References

SHOWING 1-10 OF 11 REFERENCES

Integrable deformations of Rössler and Lorenz systems from Poisson–Lie groups

Remark on integrable deformations of the Euler top

Multiple lie-poisson structures, reductions, and geometric phases for the Maxwell-Bloch travelling wave equations

SummaryThe real-valued Maxwell-Bloch equations on ℝ3 are investigated as a Hamiltonian dynamical system obtained by applying an S1 reduction to an invariant subsystem of a dynamical system on ℂ3.…

Symmetries and Properties of the Energy-Casimir Mapping in the Ball-Plate Problem

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…

Periodic orbits in the case of a zero eigenvalue

On a Hamiltonian Version of the Rikitake System

In this paper, some relevant dynamical and geometrical properties of the Rikitake dynamo system from the Poisson geometry point of view are described.

Symplectic geometry and analytical mechanics

I. Symplectic vector spaces and symplectic vector bundles.- 1: Symplectic vector spaces.- 1. Properties of exterior forms of arbitrary degree.- 2. Properties of exterior 2-forms.- 3. Symplectic forms…

Problème général de la stabilité du mouvement

The description for this book, Probleme General de la Stabilite du Mouvement. (AM-17), will be forthcoming.

A Rikitake Type System with quadratic Control

A Rikitake type system with quadratic control having a negative tuning parameter is considered and some of the geometrical and dynamical properties are analyzed.

A Rikitake type system with one control

A Rikitake type system with one control is defined and some of this geometrical and dynamical properties are pointed out.