In this manuscript, solitary wave solution of the extended (3+1)-dimensional cubic Schr \(\ddot{o}\) dinger equation are constructed by application of three mathematical methods. These methods are namely called, extended simple equation method, modified extended auxiliary equation mapping method and \((G'/G)\) -expansion method respectively. We have derived different types solutions in the form of trignometric, hypberbolic, exponential and rational functions. For the physical phenomena of the concern equation, some solutions are plotted 2-dimensional and 3-dimensional by assigning the particular values to the parameters under the constrain conditions with the assistance of Mathematica software. The extended (3+1)-dimensional cubic Schr \(\ddot{o}\) dinger equation is used to describe the propagation of pulses in highly nonlinear optical systems. Hence all results obtained by our proposed methods are novel and have not been yet reported in any literature. Moreover, this study will support physicists to envisage certain novel hypothesis and theories in nonlinear optical systems.
