查看“︁三阶刘维方程”︁的源代码

'''三阶刘维方程 '''（Third order equation）是一个三元非线性偏微分方程：<ref>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</ref>

<math> \frac{\partial u(x,y,t)}{\partial^3  xyt}=e^{u(x,y,t)}   </math>

==解析解==
三阶刘维方程具有如下解析解：

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

其中 <math>\theta(x), \psi(y) , \xi(t)</math> 为任意函数。

==行波图==
{|
|[[File:Third order Liouville equation plot 1.gif|thumb|三阶刘维方程图]]
|[[File:Third order Liouville equation plot 2.gif|thumb|三阶刘维方程图]]
|[[File:Third order Liouville equation plot 3.gif|thumb|三阶刘维方程图]]
|[[File:Third order Liouville equation plot 4.gif|thumb|三阶刘维方程图]]
|}
{|
|[[File:Third order Liouville equation plot 5.gif|thumb|三阶刘维方程图]]
|[[File:Third order Liouville equation plot 6.gif|thumb|三阶刘维方程图]]
|[[File:Third order Liouville equation plot 7.gif|thumb|三阶刘维方程图]]
|[[File:Third order Liouville equation plot 8.gif|thumb|三阶刘维方程图]]
|}
{|
|[[File:Third order Liouville equation plot 9.gif|thumb|三阶刘维方程图]]
|[[File:Third order Liouville equation plot 14.gif|thumb|三阶刘维方程图]]
|[[File:Third order Liouville equation plot 11.gif|thumb|三阶刘维方程图]]
|[[File:Third order Liouville equation plot 12.gif|thumb|三阶刘维方程图]]
|}

==参考文献==
<references/>
# *谷超豪 《[[孤立子]]理论中的[[达布变换]]及其几何应用》 上海科学技术出版社
# *阎振亚著 《复杂非线性波的构造性理论及其应用》 科学出版社 2007年
# 李志斌编著 《非线性数学物理方程的行波解》 科学出版社
#王东明著 《消去法及其应用》 科学出版社 2002
# *何青 王丽芬编著 《[[Maple]] 教程》 科学出版社 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
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