伯格斯-費希爾 方程 （Burgers Fisher）非线性偏微分方程有如下形式：

: \frac{\partial u}{\partial t}+u^2\frac{\partial u}{\partial x}-\frac{\partial^2 u}{\partial u^2}=u(1-u^2)

此偏微分方程的解为：

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

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

阿多米安近似解
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：

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+688.8tanh(x)^5+10230.tanh(x)^9-7102.tanh(x)^15-54.67tanh(x)^3-3672.tanh(x)^7)t^8+(-373.8tanh(x)^5+1491.tanh(x)^7-1.tanh(x)+39.67tanh(x)^3+3333.tanh(x)^11+429.tanh(x)^15-3036.tanh(x)^9-1881.tanh(x)^13)t^7+(132.tanh(x)^13+187.8tanh(x)^5-502.tanh(x)^11+743.5tanh(x)^9-27.67tanh(x)^3+tanh(x)-534.6tanh(x)^7)t^6+(-135.3tanh(x)^9+161.1tanh(x)^7-1.tanh(x)+42.tanh(x)^11-85.13tanh(x)^5+18.33tanh(x)^3)t^5+(-37.tanh(x)^7+33.33tanh(x)^5+14.tanh(x)^9-11.33tanh(x)^3+tanh(x))t^4+(5.tanh(x)^7-10.33tanh(x)^5+6.333tanh(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)

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