Supersymmetry and Convection-Diffusion-Reaction equations

TL;DR

This paper explores generating solutions for Convection-Diffusion-Reaction equations using Darboux transformations and discusses supersymmetric pairs, providing new methods for solving and relating these equations.

Contribution

It introduces a novel approach to generate solutions of CDR equations via Darboux transformations and examines supersymmetric pairs through similarity solutions.

Findings

Solutions of CDR equations can be generated from other solutions using Darboux transformations.

Supersymmetric pairs of CDR equations are connected through similarity solutions.

The method is demonstrated with specific reaction coefficient types.

Abstract

In this work we are concerned with generating solutions of a class of Convection-Diffusion-Reaction equation from the solutions of another CDR equation through the Darboux transformations. The method is elucidated by cases with certain types of the reaction coefficients. We have also discussed briefly supersymmetric pairs of Convection-Diffusion-Reaction equations connected through similarity solutions.