© 2022 World Scientific Publishing Company.Nonlinear evolution equations play enormous significant roles to work with complicated physical phenomena located across the nature world. The Schrödinger type equations bearing nonlinearity are important models that flourished with the wide-ranging arena concerning plasma physics, nonlinear optics, fluid flow and the theory of deep-water waves. In this exploration, we retrieve the soliton and other solutions in an appropriate form to the coupled nonlinear Schrödinger equations by means of the improved tanh method and the rational (G'/G)-expansion method. The suggested system of nonlinear Schrödinger equations is turned into a differential equation of a single variable through executing some operations. Thereupon, successful implementation of the advised techniques regains the abundant exact traveling wave solutions. The obtained solutions are figured out in the profiles of three-dimensional (3D), two-dimensional (2D) and contour by assigning suitable values of the involved unknown constants. These diverse graphical appearances enable the researchers to understand the underlying mechanisms of intricate phenomena of the leading equations. The individual performances of the employed methods are praiseworthy which deserve further application to unravel any other nonlinear partial differential equations arising in various branches of science.