The dual-core optical fiber has significant applications in optical electronics for long-wave propagation, especially in telecommunication fibers. The aim of this article is to study the parametric effects on solitary wave propagation and characteristic aspects of long-wave traveling through optical fibers by establishing some standard and wide-spectrum solutions via the improved Bernoulli sub-equation function (IBSEF) method and the new auxiliary equation (NAE) approach. The investigated solitary wave solutions are ascertained as an integration of hyperbolic, exponential, rational and trigonometric functions and can be extensively applicable in optics. The physical significance of the solutions attained is illustrated for the definite values of the included parameters through depicting the 3D profiles. The solitons profile represents different types of waves associated with the free parameters which are related to the wave number and velocity of the solutions. It turns out that the obtained solutions through both the methods are potential and might be used in further works to interpret the various fields in telecommunication fiber which can reduce casualties that ensue in essence.