纽厄尔-怀特海德方程（Newell-Whitehead equation)是一个非线性偏微分方程：

u_{t}-u_{xx}-\alphau+betau^3=0
行波解
纽厄尔-怀特海德方程有行波解：
:u(x, t) = 1/\sqrt(\beta),
:u(x, t) = -1/\sqrt(\beta),
:u(x, t) = -(1/2I)/\sqrt(-\beta)-(1/2)cot(_C1-(1/4I)\sqrt(2)x-(3/4I)*t)/\sqrt(-\beta),
: u(x, t) = -(1/2I)/\sqrt(-\beta)+(1/2)cot(_C1-(1/4I)\sqrt(2)x+(3/4I)*t)/\sqrt(-\beta),
:u(x, t) = -(1/2I)/\sqrt(-\beta)-(1/2)cot(_C1+(1/4I)\sqrt(2)x-(3/4I)*t)/\sqrt(-\beta),
:u(x, t) = -(1/2I)/\sqrt(-\beta)+(1/2)cot(_C1+(1/4I)\sqrt(2)x+(3/4I)*t)/\sqrt(-\beta),
:u(x, t) = -(1/2I)/\sqrt(-\beta)+(1/2)tan(_C1-(1/4I)\sqrt(2)x-(3/4I)*t)/\sqrt(-\beta),
: u(x, t) = -(1/2I)/\sqrt(-\beta)-(1/2)tan(_C1-(1/4I)\sqrt(2)x+(3/4I)*t)/\sqrt(-\beta),
: u(x, t) = -(1/2I)/\sqrt(-\beta)+(1/2)tan(_C1+(1/4I)\sqrt(2)x-(3/4I)*t)/\sqrt(-\beta),
:u(x, t) = -(1/2I)/\sqrt(-\beta)-(1/2)tan(_C1+(1/4I)\sqrt(2)x+(3/4I)*t)/\sqrt(-\beta),
:u(x, t) = (1/2I)/\sqrt(-\beta)+(1/2)cot(_C1-(1/4I)\sqrt(2)x-(3/4I)*t)/\sqrt(-\beta),
: u(x, t) = (1/2I)/\sqrt(-\beta)-(1/2)cot(_C1-(1/4I)\sqrt(2)x+(3/4I)*t)/\sqrt(-\beta),
:u(x, t) = (1/2I)/\sqrt(-\beta)+(1/2)cot(_C1+(1/4I)\sqrt(2)x-(3/4I)*t)/\sqrt(-\beta),
: u(x, t) = (1/2I)/\sqrt(-\beta)-(1/2)cot(_C1+(1/4I)\sqrt(2)x+(3/4I)*t)/\sqrt(-\beta),
:u(x, t) = (1/2I)/\sqrt(-\beta)-(1/2)tan(_C1-(1/4I)\sqrt(2)x-(3/4I)*t)/\sqrt(-\beta),
:u(x, t) = (1/2I)/\sqrt(-\beta)+(1/2)tan(_C1-(1/4I)\sqrt(2)x+(3/4I)*t)/\sqrt(-\beta),
: u(x, t) = (1/2I)/\sqrt(-\beta)-(1/2)tan(_C1+(1/4I)\sqrt(2)x-(3/4I)*t)/\sqrt(-\beta),
: u(x, t) = (1/2I)/\sqrt(-\beta)+(1/2)tan(_C1+(1/4I)\sqrt(2)x+(3/4I)*t)/\sqrt(-\beta),
: u(x, t) = -1/(2\sqrt(\beta))+(1/2)coth(_C1-(1/4)\sqrt(2)x-(3/4)*t)/\sqrt(\beta),
:u(x, t) = -1/(2\sqrt(\beta))-(1/2)coth(_C1-(1/4)\sqrt(2)x+(3/4)*t)/\sqrt(\beta),
:u(x, t) = -1/(2\sqrt(\beta))+(1/2)coth(_C1+(1/4)\sqrt(2)x-(3/4)*t)/\sqrt(\beta),
:u(x, t) = -1/(2\sqrt(\beta))-(1/2)coth(_C1+(1/4)\sqrt(2)x+(3/4)*t)/\sqrt(\beta),
: u(x, t) = -1/(2\sqrt(\beta))+(1/2)tanh(_C1-(1/4)\sqrt(2)x-(3/4)*t)/\sqrt(\beta),
: u(x, t) = -1/(2\sqrt(\beta))-(1/2)tanh(_C1-(1/4)\sqrt(2)x+(3/4)*t)/\sqrt(\beta),
:u(x, t) = -1/(2\sqrt(\beta))+(1/2)tanh(_C1+(1/4)\sqrt(2)x-(3/4)*t)/\sqrt(\beta),
:u(x, t) = -1/(2\sqrt(\beta))-(1/2)tanh(_C1+(1/4)\sqrt(2)x+(3/4)*t)/\sqrt(\beta),
:u(x, t) = 1/(2\sqrt(\beta))-(1/2)coth(_C1-(1/4)\sqrt(2)x-(3/4)*t)/\sqrt(\beta),
:u(x, t) = 1/(2\sqrt(\beta))+(1/2)coth(_C1-(1/4)\sqrt(2)x+(3/4)*t)/\sqrt(\beta),
:u(x, t) = 1/(2\sqrt(\beta))-(1/2)coth(_C1+(1/4)\sqrt(2)x-(3/4)*t)/\sqrt(\beta),
: u(x, t) = 1/(2\sqrt(\beta))+(1/2)coth(_C1+(1/4)\sqrt(2)x+(3/4)*t)/\sqrt(\beta),
:u(x, t) = 1/(2\sqrt(\beta))-(1/2)tanh(_C1-(1/4)\sqrt(2)x-(3/4)*t)/\sqrt(\beta),
:u(x, t) = 1/(2\sqrt(\beta))+(1/2)tanh(_C1-(1/4)\sqrt(2)x+(3/4)*t)/\sqrt(\beta),
:u(x, t) = 1/(2\sqrt(\beta))-(1/2)tanh(_C1+(1/4)\sqrt(2)x-(3/4)*t)/\sqrt(\beta),
:u(x, t) = 1/(2\sqrt(\beta))+(1/2)tanh(_C1+(1/4)\sqrt(2)x+(3/4)*t)/\sqrt(\beta)

行波图
参考文献

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