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Symmetries of the Maxwell-Bloch equations with the rotating wave approximation. (English) Zbl 1308.70018

Summary: In this paper a symplectic realization for the Maxwell-Bloch equations with the rotating wave approximation is given, which also leads to a Lagrangian formulation. We show how Lie point symmetries generate a third constant of motion for the dynamical system considered.

MSC:

70H03 Lagrange’s equations
70H05 Hamilton’s equations
70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
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