The nonlinear diffusion reaction dynamical system with quadratic and cubic nonlinearities with analytical investigations

Abstract

Our aim in this research work is to formulate the exact traveling and solitary wave solutions of nonlinear diffusion reaction (DR) equation with quadratic and cubic nonlinearities by implementing the new technique which is a modified mathematical method. We have investigated the density independent nonlinear diffusion equation with convective flux term. As a result, we have found a variety of new exact traveling and solitary wave solutions in the form of dark solitons, bright solitons, combined dark-bright solitons, traveling wave, periodic wave solutions and we also represent the physical structure of the obtained solutions by two- and three-dimensional graphics by using the Mathematica software. This work proves the power, reliability and fruitfulness of this new technique.