三階劉維方程

三階劉維方程 （Third order equation）是一個三元非線性偏微分方程：^[1]

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

解析解

三階劉維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 $\theta (x),\psi (y),\xi (t)$ 為任意函數。

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

*谷超豪《孤立子理論中的達布變換及其幾何應用》上海科學技術出版社
*閻振亞著《複雜非線性波的構造性理論及其應用》科學出版社 2007年
李志斌編著《非線性數學物理方程的行波解》科學出版社
王東明著《消去法及其應用》科學出版社 2002
*何青王麗芬編著《Maple 教程》科學出版社 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