Dark-bright solitons and the role of their interaction in breather generation

We study fundamental dark-bright solitons and the interaction of vector nonlinear Schrödinger equations in both focusing and defocusing regimes. Classification of possible types of soliton solutions is given. There are two types of solitons in the defocusing case and four types of solitons in the focusing case. The number of possible variations of two-soliton solutions depends on this classification. We demonstrate that only special types of two-soliton solutions in the focusing regime can generate breathers of the scalar nonlinear Schrödinger equation. The cases of solitons with equal and unequal velocities in the superposition are considered. Numerical simulations confirm the validity of our exact solutions.