Dynamical structure of optical soliton solutions for M-fractional paraxial wave equation by using unified technique

This study deliberates the fractional form of the paraxial wave equation, which is used to investigate the selffocusing of optical waves in nonlinear media. The truncated time M-fractional derivative is used to get rid of the fractional order in the governing model. The several optical wave pattern of the paraxial wave equation can play an insignificant role to describe the dynamics of optical soliton solutions in optics and photonics for the study of various physical processes, including the propagation of light through optical systems, such as lenses, mirror, and fiber optics. In this framework, the newly introduced unified scheme is implemented to investigate optical soliton solutions of truncated time M-fractional Paraxial Wave (tM-fPW) equation. Under some conditions, the established solutions are expressed in terms of hyperbolic, trigonometric, and rational function forms with some free parameters. For the numerical values of the free parameters, we found optical periodic wave, the interaction of periodic wave and rogue wave, breather wave, linked rogue wave, periodic rogue wave solution, etc. For a corporeal explanation of the obtained solutions, we plotted among them with 3-D, density, and contour plots and analyzed the self-focusing of an optical pulse in nonlinear media.