On traveling wave solutions of an autocatalytic reaction–diffusion Selkov–Schnakenberg system

Abstract

This paper investigates the analytical solutions of the autocatalytic reaction–diffusion Selkov–Schnakenberg system of coupled nonlinear PDEs mathematical perspective. This is a simple chemical reaction system that admits periodic solutions. The new families of exact solutions are derived which represent the autocatalyst and reactant of chemical concentrations. These exact solutions are obtained by using the technique namely as ϕ6-model expansion. Furthermore, the existence of these solutions is also discussed under different constraint conditions and variables of concentrations that are represented in hyperbolic, trigonometric, and rational forms. These results are new and effective in the physical phenomena of autocatalytic chemical reactions. For a better understanding of the physical interpretation of the solutions, the 3D and 2D graphs of some reported solutions are dispatched below for the different choices of parameters. Hence the physical description of our results may fruitful tool for investigating the further results for nonlinear wave problems in applied science.