Abundant new optical solitary waves of paraxial wave dynamical model with kerr media via new extended direct algebraic method

The new extended direct algebraic technique (EDAT) is used to investigate the rational, and soliton solution for time dependent dimension-less paraxial wave model. The wave solutions help in considerations of physical phenomena and have significant applications in engineering and physics. In optics and photonics, various optical patterns of waves can be beneficial for demonstrating the dynamics behavior of optical solutions that pertain to studying a several kind of mechanical techniques involving the flow of light via optical fibers like mirror, lenses and imaging. By applying suitable parameter values, the exact solutions are obtained with dark, bright, singular, bright-dark, periodic form by using Mathematica 11.0. The 3-D density, 2-D plot and contour plot are plotted and explored the self-focusing structure of electromagnetic waves in non-linear techniques to present a physical description of examined solutions using Matlab. The obtain soliton solutions demonstrate the non-dispersive and non-diffractive localized propagation wave packets in optical kerr media.