位势Burgers方程的自相似解和行波解
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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.
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.
[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.