Symmetries and Solutions for a Class of Advective Reaction-Diffusion Systems with a Special Reaction Term

Abstract

This paper is devoted to apply the Lie methods to a class of reaction diffusion advection systems of two interacting species u and v with two arbitrary constitutive functions f and g. The reaction term appearing in the equation for the species v is a logistic function of Lotka-Volterra type. Once obtained the Lie algebra for any form of f and g a Lie classification is carried out. Interesting reduced systems are derived admitting wide classes of exact solutions.

Keywords

• reaction-diffusion-advection equations
• symmetries
• exact solutions
• Lotka-Volterra funtctions