Systematic construction of vector solitons

We present a simple but powerful method for constructing multisolitons of the integrable Manakov (coupled nonlinear Schrodinger) equation. Our method is essentially equivalent to the inverse scattering method (ISM) with the full strength generality but without the mathematical rigor of the ISM. This makes our method appropriate for practical purposes. A closed form of matrix determinant for the N-soliton solution in a nonvanishing background is found in this way. We work out explicitly the two dark vector soliton and the three bright vector soliton cases and demonstrate their novel behaviors.