Hamiltonian flows for a reduced Maxwell–Bloch system with permanent dipole

We place a reduced Maxwell–Bloch (rMB) system with permanent dipole in a Lie algebraic framework that enables us to reveal a hierarchy of systems in involution, the first of which is the rMB model. This is done in the context of the Adler–Kostant–Symes theorem. We provide the Hamiltonian functions for the commuting flows and establish an infinite number of conservation laws.