Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

# Notes on the Lie Symmetry Exact Explicit Solutions for Nonlinear Burgers' Equation

Version 1 : Received: 12 August 2019 / Approved: 13 August 2019 / Online: 13 August 2019 (07:23:24 CEST)
Version 2 : Received: 30 August 2019 / Approved: 1 September 2019 / Online: 1 September 2019 (03:03:39 CEST)
Version 3 : Received: 28 November 2021 / Approved: 29 November 2021 / Online: 29 November 2021 (12:00:06 CET)

How to cite: Sun, B. Notes on the Lie Symmetry Exact Explicit Solutions for Nonlinear Burgers' Equation. Preprints 2019, 2019080150 (doi: 10.20944/preprints201908.0150.v3). Sun, B. Notes on the Lie Symmetry Exact Explicit Solutions for Nonlinear Burgers' Equation. Preprints 2019, 2019080150 (doi: 10.20944/preprints201908.0150.v3).

## Abstract

In light of Liu \emph{at el.}'s original works, this paper revisits the solution of Burgers's nonlinear equation $u_t=a(u_x)^2+bu_{xx}$. The study found two exact and explicit solutions for groups $G_4$ and $G_6$, as well as a general solution. A numerical simulation is carried out. In the appendix a Maple code is provided

## Keywords

Lie group; Burgers equation; exact solution; general solution; elementary function

## Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

Comment 1
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author
Comment: some typos are corrected and contents are rearranged
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