Algebraic methods in the study of systems of the reaction-diffusion type

TL;DR

This paper explores algebraic techniques, specifically Lie algebras, to analyze nonlinear reaction-diffusion systems like Gierer-Meinhardt models, deriving exact solutions and comparing them with numerical results.

Contribution

It introduces an algebraic approach using Lie algebras to find exact solutions for reaction-diffusion systems, enhancing analytical methods in this field.

Findings

Derivation of special exact solutions for reaction-diffusion models

Comparison of algebraic solutions with numerical simulations

Demonstration of Lie algebra methods' effectiveness in nonlinear systems

Abstract

Nonlinear systems of the reaction-diffusion type, including Gierer-Meinhardt models of autocatalysis, are studied by using Lie algebras coming from the prolongation structure. The consequences of this analytical approach, as the determination of special exact solutions, are compared with the corresponding results obtained via numerical simulations.