© 2022In the field of maritime transport, motion and energy, the dynamics of deep-sea waves is one of the major problems in ocean science. A mathematical modeling of dynamics of solitary waves in deep sea under the two-layer stratification leads to NLS equation, and consequently, the interaction two of them can be formulated by coupled NLS equation. In this work, extended auxiliary equation and the exp(−ϖ(χ))-expansion methods are employed to make the optical solutions of the Manakov model of coupled NLS equation. The methods used in this paper, in addition to providing the analysis of individual wave solutions, also provide general optical solutions. Some previously known solutions can be obtained by some special selections of parameters obtained by solving systems of algebraic equations. At this stage, it is more practical and convenient to apply methods with a symbolic calculation system.