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      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

       

      R SINUVASAN1 K M TAMIZHMANI1 P G L LEACH1 2

      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
    • Dates

       
  • Pramana – Journal of Physics | News

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