Bi-Hamiltonian structure and homoclinic orbits of the Maxwell–Bloch equations with RWA

In this paper, a bi-Hamiltonian structure of the Maxwell–Bloch equations with the rotating wave approximation (RWA) is given explicitly. Then by the Casimir function theory, the existence of homoclinic orbits is proved rigorously, which is a sign causing chaotic behavior in the Maxwell–Bloch equations, and hence supports the previous numerical results.