Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 038, 14 pages      math-ph/0603071

On the Generalized Maxwell-Bloch Equations

Pavle Saksida
Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Slovenia

Received December 01, 2005, in final form March 05, 2006; Published online March 27, 2006

A new Hamiltonian structure of the Maxwell-Bloch equations is described. In this setting the Maxwell-Bloch equations appear as a member of a family of generalized Maxwell-Bloch systems. The family is parameterized by compact semi-simple Lie groups, the original Maxwell-Bloch system being the member corresponding to SU(2). The Hamiltonian structure is then used in the construction of a new family of symmetries and the associated conserved quantities of the Maxwell-Bloch equations.

Key words: Maxwell-Bloch equations; Hamiltonian structures; symmetries; conserved quantities.

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