Dark-dark and dark-bright soliton interactions in the two-component defocusing nonlinear Schrödinger equation

We use the Inverse Scattering Transform machinery to construct multisoliton solutions to the 2-component defocusing nonlinear Schrödinger equation. Such solutions include dark-dark solitons, which have dark solitonic behaviour in both components, as well as dark-bright soliton solutions, with one dark and one bright component. We then derive the explicit expressions of two soliton solutions for all possible cases: two dark-dark solitons, two dark-bright solitons, and one dark-dark and one dark-bright soliton. Finally, we determine the long-time asymptotic behaviours of these solutions, which allows us to obtain explicit expressions for the shifts in the phases and in the soliton centers due to the interactions.