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Preserved in Portico This version is not peer-reviewed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)
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. https://doi.org/10.20944/preprints201908.0150.v3 Sun, B. Notes on the Lie Symmetry Exact Explicit Solutions for Nonlinear Burgers' Equation. Preprints 2019, 2019080150. https://doi.org/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
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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