On a Hamilton-Poisson Approach of the Maxwell-Bloch Equations with a Control

被引：14

作者：

Lazureanu, Cristian ^{[1
]}

机构：

[1] Politehn Univ Timisoara, Dept Math, PiataVictorei, 2, Timisoara 300006, Romania

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2017年 / 20卷 / 03期

关键词：

Maxwell-Bloch equations; Hamiltonian dynamics; Stability; Energy Casimir mapping; Periodic orbits; ROTATING WAVE APPROXIMATION; SYSTEM; INTEGRABILITY; STABILITY; VERSION; ORBITS;

D O I：

10.1007/s11040-017-9251-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the 3D real-valued Maxwell-Bloch equations with a parametric control given by. x = y + az + byz, y = xz, z = -xy ( a, b is an element of R). We give two Lie-Poisson structures of this system that are related with well-known Lie algebras. Moreover, we construct infinitely many Hamilton-Poisson realizations of this system. We also analyze the stability of the equilibrium points, as well as the existence of periodic orbits. In addition, we emphasize some connections between the energy-Casimir mapping of the considered system and the above-mentioned dynamical elements.

引用

页数：22

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