An Analytical Studies of the Reaction- Diffusion Systems of Chemical Reactions

Reaction–diffusion systems are seen in not only many fields of science but also social behaviorus. In this work, Schnakenberg, Brusselator and Lengyel–Epstein models are considered that are the best known the chemical reaction–diffusion models and are also seen in a large scale of applications in biological or biochemical processes. Due to its importance in science and applications, for the considered models, till now the numerical and approximate solutions are obtained whereas the exact solutions in the explicit form were not obtained literature to our knowledge. Our main aim is to fill this gap by revealing their exact solutions. To obtain the exact solutions, the ansatz-based methods are considered in a novel way. The obtained results have a major role in the literature so that the considered models are seen in a large scale of applications not only chemical but also biological or biochemical processes.