Symmetries and Solutions for Some Classes of Advective Reaction–Diffusion Systems

Abstract

In this paper, we consider some reaction–advection–diffusion systems in order to obtain exact solutions via a symmetry approach. We write the determining system of a general class. Then, for particular subclasses, we obtain special forms of the arbitrary constitutive parameters that allow us to extend the principal Lie algebra. In some cases, we write the corresponding reduced system and we find special exact solutions.

Keywords

• reaction–diffusion–advection equations
• symmetries
• exact solutions