Analysis of mixed soliton solutions for the nonlinear Fisher and diffusion dynamical equations under explicit approach

In this study, with the help of improved exp (-Φ(η))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(-\Phi (\eta ))$$\end{document}-function method, we explored the soliton solutions for the well-known nonlinear Fisher and nonlinear diffusion dynamical equations. Both nonlinear equations are useful for studying fluid dynamics, biology population models, plasma, fiber optics and crystallization. Our obtained results are in the form of singular bright solitons, combined bright-dark solitons, singular dark solitons, kink wave solitons, and anti-kink solitons as well as the physical structure of the extracted solutions as drawn by three-dim graphically by utilizing numerical simulation. The method is applied on two different nonlinear models, which reveal the use and simplicity of the method. It has been verified that the proposed technique yields a wide range of solutions and provides a more powerful computational approach for investigate the nonlinear evolution equations in engineering and the mathematical sciences. Our extracted results are interesting, more general, some novel and will play important role in various field of science such as nonlinear optics, quantum physics, nonlinear dynamics, laser optics, fiber optics, plasma physics, soliton wave theory, communicational system and field of engineering. The extracted results demonstrated that the utilized approach is effective, powerful, and efficient for soliton results to the nonlinear evolution equations.