• Algebraic resolution of the Burgers equation with a forcing term

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/088/05/0074

• # Keywords

Lie algebra; Burgers equation; symmetry reduction

• # Abstract

We introduce an inhomogeneous term, $f (t,x)$, into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions $f (t,x)$ which depend nontrivially on both $t$ and $x$, we find that there is just one symmetry. If $f$ is a function of only $x$, there are three symmetries with the algebra $sl(2,R)$. When $f$ is a function of only $t$ , there are five symmetries with the algebra $sl(2,R)\oplus_{s} 2A_1$. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.

• # Author Affiliations

1. Department of Mathematics, Pondicherry University, Kalapet 605 014, India
2. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, Republic of South Africa and Institute for Systems Science, Department of Mathematics, Durban University of Technology, P.O. Box 1334, Durban 4000, Republic of South Africa

• # Pramana – Journal of Physics

Volume 94, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019