Comments on the Paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation”

Roman Cherniha

doi:10.3390/sym12060900

Abstract

This comment is devoted to the paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation” (Symmery, 2020, vol.12, 170), in which several results are either incorrect, or incomplete, or misleading.

Highlights

The recently published paper [1] is devoted to Lie symmetry analysis, exact solutions, and conservation laws of the equation ut = u xx + uyy + uu x + uuy + u(u − δ)(1 − u)
It should be noted that the family of solutions (12) of the (1+1)-dimensional BFN equation was found for the first time in [9] using a generalized conditional symmetry, and both families of solutions (11) and (12) were firstly constructed in [10] using Q-conditional symmetries
All the reduced equations were analyzed with the aim to find their exact solutions and to transform the latters into solutions of the BFN Equation (1)

Summary

Introduction

2. Lie Symmetries, Optimal Subalgebras and Exact Solutions (1 − b)/ 1 + b2 present the four-parameter families of the exact solutions of the BFN Equation (1). It should be noted that the family of solutions (12) of the (1+1)-dimensional BFN equation was found for the first time in [9] using a generalized conditional symmetry, and both families of solutions (11) and (12) were firstly constructed in [10] using Q-conditional symmetries.

Results

Conclusion