This article is cited in 4 papers

Stability and Integrability Aspects for the Maxwell–Bloch Equations with the Rotating Wave Approximation

Ioan Caşu^ab, Cristian Lăzureanu<sup>ab

a</sup> Department of Mathematics, West University of Timişoara, Bd. V. Pârvan, Nr. 4, 300223 Timişoara, România
^b Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei, Nr. 2, 300006 Timişoara, România

Abstract: Infinitely many Hamilton–Poisson realizations of the five-dimensional real valued Maxwell–Bloch equations with the rotating wave approximation are constructed and the energy-Casimir mapping is considered. Also, the image of this mapping is presented and connections with the equilibrium states of the considered system are studied. Using some fibers of the image of the energy-Casimir mapping, some special orbits are obtained. Finally, a Lax formulation of the system is given.

Keywords: Maxwell–Bloch equations, Hamiltonian dynamics, energy-Casimir mapping, homoclinic orbits, periodic orbits, elliptic functions.

MSC: 37J25, 37J45, 33E05

Received: 31.10.2016
Accepted: 12.12.2016

Language: English

DOI: 10.1134/S1560354717020010

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