三阶刘维方程

三阶刘维方程 （Third order equation）是一个三元非线性偏微分方程：^[1]

${\frac {\partial u(x,y,t)}{\partial ^{3}xyt}}=e^{u(x,y,t)}$

解析解

三阶刘维方程具有如下解析解：

u(x,y,t)={\frac {-6*\theta '(x)*\psi '(y)*\xi '(t)}{(\theta (x)+\psi (y)+\xi (t))^{3}}}

其中 $\theta (x),\psi (y),\xi (t)$ 为任意函数。

[1]
Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS,（《非线性偏微分方程手册》） SECOND EDITION p540 CRC PRESS

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