Abstract
In this paper, the time incapable illimitable paraxial wave equation which is used in Kerr-media is being investigated. The paraxial wave equation has important applications in the light beam interaction within the ripple unit and also in calculation of the light emission outside the fluctuation. We have applied two techniques, namely, He's variational and Hirota bilinear techniques to extract the diversity of optical wave structures. The diversity of the wave solutions include the three-wave hypothesis, periodic cross kink, lump periodic, mixed type wave solutions and breather wave. The 3D, 2D, and their corresponding contour plots of the earned solutions are successfully drawn for the real, and imaginary behaviors by selecting the suitable values of parameters.