Dark-dark solitons, soliton molecules and elastic collisions in the mixed three-level coupled Maxwell–Bloch equations.

We study the integrable three-level coupled Maxwell–Bloch equations with the mixed focusing-defocusing case. The n -fold Darboux transformation is constructed on basis of a linear 3 × 3 matrix eigenvalue problem. As an application, the n -dark-dark soliton solution in a simple determinant form is presented and the asymptotic behavior of the n -dark-dark soliton solution is rigorously given. In particular, under the resonant mechanism, the unusual dark-dark soliton molecules which represent the soliton bound states are analytically demonstrated. The double- and triple-dark-dark soliton molecules that are composed of two and three solitons propagating with identical velocities are graphically shown, respectively. The elastic collisions between a double- or triple-dark-dark soliton molecule and a usual dark-dark soliton, and the elastic collision of two double-dark-dark soliton molecules are discussed via the standard asymptotic analysis method. • The n-dark-dark soliton solution is derived. • The unusual dark-dark soliton molecules are analytically demonstrated. • The elastic collisions are discussed via the asymptotic analysis method. [ABSTRACT FROM AUTHOR]