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.
Citation:
Ioan Caşu, Cristian Lăzureanu, “Stability and Integrability Aspects for the Maxwell–Bloch Equations with the Rotating Wave Approximation”, Regul. Chaotic Dyn., 22:2 (2017), 109–121
\Bibitem{CasLaz17}
\by Ioan Ca{\c s}u, Cristian L{\u a}zureanu
\paper Stability and Integrability Aspects for the Maxwell–Bloch Equations with the Rotating Wave Approximation
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 2
\pages 109--121
\mathnet{http://mi.mathnet.ru/rcd245}
\crossref{https://doi.org/10.1134/S1560354717020010}
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Linking options:
https://www.mathnet.ru/eng/rcd245
https://www.mathnet.ru/eng/rcd/v22/i2/p109
This publication is cited in the following 4 articles:
Remus-Daniel Ene, Nicolina Pop, Marioara Lapadat, Luisa Dungan, “Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method”, Mathematics, 10:21 (2022), 4118
Remus-Daniel Ene, Nicolina Pop, Marioara Lapadat, “Approximate Closed-Form Solutions for the Rabinovich System via the Optimal Auxiliary Functions Method”, Symmetry, 14:10 (2022), 2185
M. R. Candido, J. Llibre, C. Valls, “New symmetric periodic solutions for the Maxwell-Bloch differential system”, Math. Phys. Anal. Geom., 22:2 (2019), 16
Lazureanu C., “On a Hamilton-Poisson Approach of the Maxwell-Bloch Equations With a Control”, Math. Phys. Anal. Geom., 20:3 (2017), 20