Solutions for Multitime Reaction–Diffusion PDE

Abstract

A previous paper by our research group introduced the nonlinear multitime reaction–diffusion PDE (with oblique derivative) as a generalized version of the single-time model. This paper states and uses some hypotheses that allow the finding of some important explicit families of the exact solutions for multitime reaction–diffusion PDEs of any dimension that have a multitemporal directional derivative term. Some direct methods for determining the exact solutions of nonlinear PDEs from mathematical physics are presented. In the single-time case, our methods present many advantages in comparison with other known approaches. Particularly, we obtained classes of ODEs and classes of PDEs whose solutions generate solutions of the multitime reaction–diffusion PDE.