Soliton Solution of the Integrable Coupled Nonlinear Schrodinger Equation of Manakov Type

The soliton solution of the integrable coupled nonlinear Schrodinger equa- tion (NLS) of Manakov typeisinvestigated by using Zakharov-Shabat (ZS) scheme. We get the bright N-solitons solution by solving the integrable un- coupled NLS of Manakov type. We also find that there is an elastic collision of the bright N-solitons.