摘要
研究了位势Burgers方程的自相似解和行波解.找到了位势Burgers方程所接受的伸缩变换群,从而找到了该方程的自相似解.利用函数变换法把非线性二阶偏微分方程——位势Burgers方程转化成Bernoulli方程,且求出了位势Burgers方程的行波解.
The scaling group admitted by potential Burgers equation is found,moreover the self-similar solution to potential Burgers equation is also given.On the other hand,the nonlinear second-order partial differential equation-potential Burgers equation is converted to Bernoulli equation by using function transformation method,finally the travelling wave solution of potential Burgers equation is presented.
引文
[1]王明亮.位势Burgers方程的对称及应用[J].兰州大学学报(自然科学版),1993(4):14-18.
[2]田畴.李群及其在微分方程中的应用[M].北京:科学出版社,2001:224-226.
[3] IBRAGIMOV N H.CRC handbook of Lie group analysis of differential equations:symmetries exact solutions and conservation law[M].Boca Raton:CRC Press,1994:183-184.
[4] MELESHKO S V.Methods for constructing exact solutions of partial differential equations:mathematical and analytical techniques with applications to engineering[M].New York:Springer,2005:52-58.
[5] OVSIANNIKOV L V.Group analysis of differential equations[M].New York:Academic Press,1982:68-72.
[6] GRIGORIEV Y N,IBRAGIMOV N H,KOVALEV V F,et al.Symmetries of integro-differential equations:with applications in mechanics and plasma physics[M].New York:Springer,2010:27-29.
[7] ZHOU L Q,MELESHKO S V.Group analysis of integro-differential equations describing stress relaxation behavior of onedimensional viscoelastic materials[J].International Journal of Non-Linear Mechanics,2015,77:223-231.
[8] LIN F B,FLOOD A E,MELESHKO S V.Exact solutions of population balance equation[J].Communications in Nonlinear Science and Numerical Simulation,2016,36:378-390.
[9]林府标.Bergers方程的一类自相似解[J].数学的实践与认识,2016,46(9):241-245.