查看“︁伯格斯-费希尔方程”︁的源代码

[[File:Burgers Fisher PDE 3d Maple plot.png|thumb|right|300px|Burgers Fisher PDE 3d Maple 图]]
[[File:Burgers Fisher pde Maple animation.gif|right|300px|Burgers Fisher pde Maple 动画]]
[[File:Burgers Fisher PDE Maple plot.png|thumb|right|300px|Burgers Fisher PDE Maple 图]]
'''伯格斯-費希爾 方程''' （Burgers Fisher）非线性偏微分[[方程]]有如下形式：<ref>Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p123-133 Equations Academy Press</ref>

:<math> \frac{\partial u}{\partial t}+u^2*\frac{\partial u}{\partial x}-\frac{\partial^2 u}{\partial u^2}=u*(1-u^2) </math>

此偏微分方程的解为：

<math>u(x,t)=\frac{1}{2}*\sqrt{1-tanh(\frac{x}{3}-\frac{10t}{9})}</math>

<math>g[5] := {u(x, t) = _C6*(exp(_C1-(1/3)*x+(2/3)*t))^3}</math>

==阿多米安近似解==
[[File:Burgers Fisher equation tanh Adomian plot.gif|left|350px]]
利用[[阿多米安分解法]]可求得Burgers-Fisher方程的在[[柯西问题]] u(0)=sin(x) 初始条件下的级数展开近似解：<ref>Inna Shingareve Carlos Lizarraga Celaya，Solving Nonlinear Partial Differential Equations with Maple and Mathematica p230-236, Springer</ref>

pa := (-1.*tanh(x)-82360.*tanh(x)^13+73.*tanh(x)^3-1195.*tanh(x)^5+8233.*tanh(x)^7-29990.*tanh(x)^9+63510.*tanh(x)^15-26980.*tanh(x)^17+4862.*tanh(x)^19+63850.*tanh(x)^11)*t^9+(14650.*tanh(x)^13-16170.*tanh(x)^11+tanh(x)+1430.*tanh(x)^17+688.8*tanh(x)^5+10230.*tanh(x)^9-7102.*tanh(x)^15-54.67*tanh(x)^3-3672.*tanh(x)^7)*t^8+(-373.8*tanh(x)^5+1491.*tanh(x)^7-1.*tanh(x)+39.67*tanh(x)^3+3333.*tanh(x)^11+429.*tanh(x)^15-3036.*tanh(x)^9-1881.*tanh(x)^13)*t^7+(132.*tanh(x)^13+187.8*tanh(x)^5-502.*tanh(x)^11+743.5*tanh(x)^9-27.67*tanh(x)^3+tanh(x)-534.6*tanh(x)^7)*t^6+(-135.3*tanh(x)^9+161.1*tanh(x)^7-1.*tanh(x)+42.*tanh(x)^11-85.13*tanh(x)^5+18.33*tanh(x)^3)*t^5+(-37.*tanh(x)^7+33.33*tanh(x)^5+14.*tanh(x)^9-11.33*tanh(x)^3+tanh(x))*t^4+(5.*tanh(x)^7-10.33*tanh(x)^5+6.333*tanh(x)^3-1.*tanh(x))*t^3+(-3.*tanh(x)^3+tanh(x)+2.*tanh(x)^5)*t^2+(-1.*tanh(x)+tanh(x)^3)*t+tanh(x)

==参考文献==
<references/>
# *谷超豪 《[[孤立子]]理论中的[[达布变换]]及其几何应用》 上海科学技术出版社
# *阎振亚著 《复杂非线性波的构造性理论及其应用》 科学出版社 2007年
# 李志斌编著 《非线性数学物理方程的行波解》 科学出版社
#王东明著 《消去法及其应用》 科学出版社 2002
# *何青 王丽芬编著 《[[Maple]] 教程》 科学出版社 2010 ISBN 9787030177445
#Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press
# Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
#Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
#Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
#Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
#Dongming Wang, Elimination Practice,Imperial College Press 2004
# David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
# George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759

{{非线性偏微分方程}}

[[category:非线性偏微分方程]]