2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94493The general multi-soliton solution of the integrable coupled nonlinear Schrodinger equation (NLS) of Manakov type is investigated by using Zakharov-Shabat (ZS) scheme. We get the bright and dark multi-soliton solution using inverse scattering method of ZS scheme. Elastic and inelastic collision of N-solitons solution of the equation are also discussed.15 pages, LaTeX2e, PACS 42.65SfExactly Solvable and Integrable SystemsHigh Energy Physics - TheoryMathematical PhysicsDynamical SystemsPattern Formation and SolitonsMulti-soliton Solution of the Integrable Coupled Nonlinear Schrodinger Equation of Manakov Typetext