Optical solitary waves solutions of the eight-order dispersive Schrödinger wave equation

The nonlinear dispersive eighth-order Schr & ouml;dinger equation is a mathematical equation that describes the behaviour of complex wave phenomena in specific physical systems. It is utilised in the fields of nonlinear optics and wave propagation. This article examines the eighth-order dispersive nonlinear Schr & ouml;dinger equation, using the sine-cosine approach to extract optical solitons expressed as sine and cosine functions. The sine-cosine method gives a systematic and efficient strategy for obtaining solitary wave solutions without requiring extensive computational resources. By expanding the solution in terms of sine and cosine functions, the technique transforms the problem into solving a system of algebraic equations, which is often more computationally tractable than other methods. Then solving the obtained algebraic system, the desired solutions are archived. The solutions obtained are then simulated using Mathematica. The results demonstrate bright, bell-shaped and periodic optical solitons for specific parameter values. The obtained results are depicted via 3D and 2D graphs.