Similarity solutions of Reaction-Diffusion equation with space- and time-dependent diffusion and reaction terms

TL;DR

This paper develops a method to find exact solutions for generalized reaction-diffusion equations with variable coefficients by reducing them to solvable ordinary differential equations using similarity variables.

Contribution

It introduces a similarity-based approach to derive exact solutions for reaction-diffusion equations with space- and time-dependent terms, expanding solvable models.

Findings

Derived several exactly solvable reaction-diffusion systems

Reduced complex PDEs to known solvable ODEs

Provided examples demonstrating the method's effectiveness

Abstract

We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction-diffusion systems. Several representative examples of exactly solvable reaction-diffusion equations are presented.