Some New Non-Travelling Wave Solutions of the Fisher Equation with Nonlinear Auxiliary Equation

Abstract

We have generated many new non-travelling wave solutions by executing the new extended generalized and improved (G'/G)-Expansion Method. Here the nonlinear ordinary differential equation with many new and real parameters has been used as an auxiliary equation. We have investigated the Fisher equation to show the advantages and effectiveness of this method. The obtained non-travelling solutions are expressed through the hyperbolic functions, trigonometric functions and rational functional forms. Results showing that the method is concise, direct and highly effective to study nonlinear evolution equations those are in mathematical physics and engineering.

Chaotic Phenomena, Sensitivity Analysis, Bifurcation Analysis, and New Abundant Solitary Wave Structures of The Two Nonlinear Dynamical Models in Industrial Optimization

“…. The (i) 3D, (ii) contour, and (iii) 2D shapes that have bell-shaped solitons for Equation (33) with the given set of parameters.…”

“…In addition, the (G ′ /G)-expansion technique was introduced by Wang et al for describing the outcomes of NLPDEs [32]. Many investigators have applied this technique in their investigative works [33][34][35][36][37][38][39][40]. In addition to these, many investigators aspired to look for other alternatives that are more diligent and better than the former technique.…”