Algebraic resolution of the Burgers equation with a forcing term

被引：0
|
作者：
R SINUVASAN
K M TAMIZHMANI
P G L LEACH
机构：
[1] Pondicherry University,Department of Mathematics
[2] Durban University of Technology,Permanent addresses: School of Mathematics, Statistics and Computer Science, University of KwaZulu
来源：
Pramana | 2017年 / 88卷
关键词：
Lie algebra; Burgers equation; symmetry reduction.; 02.20.Sv; 02.30.Ik; 02.30.Jr;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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) ⊕s2A1. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.
引用
收藏
相关论文
共 50 条
  • [1] Algebraic resolution of the Burgers equation with a forcing term
    Sinuvasan, R.
    Tamizhmani, K. M.
    Leach, P. G. L.
    [J]. PRAMANA-JOURNAL OF PHYSICS, 2017, 88 (05):
  • [2] KINK WAVE SOLUTIONS TO KDV-BURGERS EQUATION WITH FORCING TERM
    Chukkol, Yusuf Buba
    Muminov, Mukhiddin
    [J]. COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2020, 35 (02): : 685 - 695
  • [3] THE BURGERS EQUATION WITH POISSON RANDOM FORCING
    Bakhtin, Yuri
    [J]. ANNALS OF PROBABILITY, 2013, 41 (04): : 2961 - 2989
  • [4] The shock wave solution to the Riemann problem for the Burgers equation with the linear forcing term
    Zhang, Ting
    Shen, Chun
    [J]. APPLICABLE ANALYSIS, 2016, 95 (02) : 283 - 302
  • [5] Comment on "Connection between the Burgers equation with an elastic forcing term and a stochastic process"
    Garbaczewski, Piotr
    [J]. PHYSICAL REVIEW E, 2006, 74 (02):
  • [6] The Burgers equation under deterministic and stochastic forcing
    Ablowitz, MJ
    DeLillo, S
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 1996, 92 (3-4) : 245 - 259
  • [7] Invariant measures for Burgers equation with stochastic forcing
    Khanin, WEK
    Mazel, A
    Sinai, Y
    [J]. ANNALS OF MATHEMATICS, 2000, 151 (03) : 877 - 960
  • [8] APPLICATION OF EXTENDED TANH FUNCTION METHOD ON KdV-BURGERS EQUATION WITH FORCING TERM
    Abazari, Reza
    [J]. ROMANIAN JOURNAL OF PHYSICS, 2014, 59 (1-2): : 3 - 11
  • [9] Comment on 'Connection between the Burgers equation with an elastic forcing term and a stochastic process' -: Reply
    Moreau, E.
    Vallee, O.
    [J]. PHYSICAL REVIEW E, 2006, 74 (02):
  • [10] Asymptotics for viscous Burgers equation under impulsive forcing
    Dwivedi, Kanchan
    Engu, Satyanarayana
    Berke, Venkatramana P.
    Sahoo, Manas Ranjan
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2024, 65 (08)
12345