Bi-Hamiltonian structure and homoclinic orbits of the Maxwell--Bloch equations with RWA

DOI10.1016/J.CHAOS.2004.01.002zbMath1067.37092OpenAlexW1987836825MaRDI QIDQ1772578

Debin Huang

Publication date: 21 April 2005

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2004.01.002

zbMATH Keywords

chaotic behaviornonlinear opticscomplete integrabilityrotating wave approximationsmale horseshoeCasimir function theory

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Nonlinear first-order PDEs (35F20) Lasers, masers, optical bistability, nonlinear optics (78A60)

Related Items (5)

Stability and integrability aspects for the Maxwell-Bloch equations with the rotating wave approximation ⋮ On a Hamilton-Poisson approach of the Maxwell-Bloch equations with a control ⋮ Nonstandard separation of variables for the Maxwell-Bloch conservative system ⋮ Symmetries of the Maxwell-Bloch equations with the rotating wave approximation ⋮ The stability problem and special solutions for the 5-components Maxwell-Bloch equations

Cites Work

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• On the generalized Hamiltonian structure of 3D dynamical systems
• Global solvability of the Maxwell-Bloch equations from nonlinear optics
• Numerical solutions of the Maxwell-Bloch laser equations
• The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system
• On the Dynamics of Lotka--Volterra Equations Having an Invariant Hyperplane
• Bi-Hamiltonian systems and Lotka - Volterra equations: a three-dimensional classification
• Simple evaluation of Casimir invariants in finite-dimensional Poisson systems
• One solution of the 3D Jacobi identities allows determining an infinity of them

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