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

Abstract

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.