General N-Dark-Dark Solitons in the Coupled Nonlinear Schrodinger Equations

N-darkdark solitons in the integrable coupled NLS equations are derived by the KP-hierarchy reduction method. These solitons exist when nonlinearities are all defocusing, or both focusing and defocusing nonlinearities are mixed. When these solitons collide with each other, energies in both components of the solitons completely transmit through. This behavior contrasts collisions of brightbright solitons in similar systems, where polarization rotation and soliton reflection can take place. It is also shown that in the mixed-nonlinearity case, two darkdark solitons can form a stationary bound state.