In this paper the optical pulses and other solitary wave solutions are extracted in dual-core optical fibers. The decoupled nonlinear Schrodinger equation is taken as a controlling equation. The model is composed of group-velocity dispersion and mismatch, linear coupling coefficient, and nonlinear refractive index. The optical pulses in different shapes like dark, bright, singular, and combined solitons by application of the generalized exponential rational function method and the new extended direct algebraic method . Furthermore, a stack of exponential, hyperbolic, and trigonometric function wave solitary solutions is magnificently constructed by means of the indicated schemes. Some of the acquired wave solutions are characterized graphically in 3D, contour, and 2D shapes to illustrate the dynamical behavior. A comparison of the results of this study with those found in the literature shows that the current wave solutions are innovative and diverse, which boosts the impressive performance of the utilized methodologies. Complicated models in a wide range of physical circumstances may benefit from the strategies presented. We anticipate that this study will be useful to a wide range of engineering modellers.