Group classification of systems of non-linear reaction-diffusion equations with general diffusion matrix. I. Generalized Landau-Ginzburg equations

TL;DR

This paper develops a method for classifying symmetries of generalized reaction-diffusion systems with complex diffusion matrices, specifically applied to generalized Landau-Ginzburg equations, enhancing understanding of their invariant properties.

Contribution

It introduces a new approach for group classification of reaction-diffusion systems with general diffusion matrices, extending previous methods to more complex equations.

Findings

Classified symmetries of generalized Landau-Ginzburg equations.

Developed a systematic approach for reaction-diffusion systems with complex diffusion matrices.

Enhanced understanding of invariant properties of these systems.

Abstract

Group classification of the generalized complex Ginzburg-Landau equations is presented. An approach to group classification of systems of reaction-diffusion equations with general diffusion matrix is developed.