查菲 - 堙方特方程

查菲 - 堙方特方程（Chaffee-Infante equation）是一个非线性偏微分方程：^[1]

$u_{t}-u_{xx}+\lambda *(u^{3}-u)=0$

解析解

u(x,t)=-1/2-(1/2*I)*cot(_{C}1-(1/4)*{\sqrt {(}}-2*\lambda )*x+(3/4*I)*\lambda *t)

u(x,t)=-1/2-(1/2*I)*tan(_{C}1-(1/4)*{\sqrt {(}}-2*\lambda )*x-(3/4*I)*\lambda *t)

u(x,t)=-1/2+(1/2*I)*cot(_{C}1+(1/4)*{\sqrt {(}}-2*\lambda )*x-(3/4*I)*\lambda *t)

u(x,t)=-1/2+(1/2*I)*tan(_{C}1+(1/4)*{\sqrt {(}}-2*\lambda )*x+(3/4*I)*\lambda *t)

u(x,t)=-1/2-(1/2)*coth(_{C}1-(1/4)*{\sqrt {(}}2)*{\sqrt {(}}\lambda )*x+(3/4)*\lambda *t)

u(x,t)=-1/2+(1/2)*tanh(_{C}1-(1/4)*{\sqrt {(}}2)*{\sqrt {(}}\lambda )*x-(3/4)*\lambda *t)

u(x,t)=1/2-(1/2*I)*cot(_{C}1-(1/4)*{\sqrt {(}}-2*\lambda )*x-(3/4*I)*\lambda *t)

u(x,t)=1/2-(1/2*I)*tan(_{C}1+(1/4)*{\sqrt {(}}-2*\lambda )*x+(3/4*I)*\lambda *t)

u(x,t)=1/2-(1/2)*coth(_{C}1-(1/4)*{\sqrt {(}}2)*{\sqrt {(}}\lambda )*x-(3/4)*\lambda *t)

Chaffe-Infante equation traveling wave plot

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