  The integrable vector nonlinear Schrodinger (vector NLS) equation is
investigated by using Zakharov-Shabat (ZS) scheme. We get a Lax pair
formulation of the vector NLS model. Multi-soliton solution of the equation is
also derived by using inverse scattering method of ZS scheme. We also find that
there is an elastic and inelastic collision of the bright and dark
multi-solitons of the system.
