Group classification of systems of non-linear reaction-diffusion equations with general diffusion matrix. II. Generalized Turing systems

TL;DR

This paper classifies symmetries of coupled nonlinear reaction-diffusion systems with various diffusion matrices, extending previous work to include singular matrices and additional derivative terms, aiding in understanding pattern formation.

Contribution

It provides a comprehensive group classification for reaction-diffusion systems with general diffusion matrices, including singular cases and extra derivative terms, advancing symmetry analysis in this field.

Findings

Classification of symmetries for systems with diagonal diffusion matrices

Description of symmetries for systems with singular diffusion matrices

Analysis of systems with additional first order derivative terms

Abstract

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.