刘维方程(Liouville equation)是一个非线性偏微分方程：

::::::::::uu_{xt}-uu_{x}+\alpha*u^3 = 0

解析解
:pu[2] := ln(-3.4101973587048390836csc(1.32+1.4934776966447732662x^1.2+1.6440433652163821333*t^1.2)^2)
:pu[3] := ln(-3.4101973587048390836csch(1.32+1.4934776966447732662x^1.2+1.6440433652163821333*t^1.2)^2)
:pu[4] := ln(-3.4101973587048390836sec(1.32+1.4934776966447732662x^1.2+1.6440433652163821333*t^1.2)^2)
:pu[5] := ln(3.4101973587048390836sech(1.32+1.4934776966447732662x^1.2+1.6440433652163821333*t^1.2)^2)
:pu[9] := ln(-3.4101973587048390836-3.4101973587048390836cot(1.32+1.4934776966447732662x^1.2+1.6440433652163821333*t^1.2)^2)
:pu[12] := ln(3.4101973587048390836-3.4101973587048390836tanh(1.32+1.4934776966447732662x^1.2+1.6440433652163821333*t^1.2)^2)
:pu[13] := ln(4.1031336303472692620-4.1031336303472692620coth(1.44+1.6440433652163821333x^1.2+1.7969454312181156991*t^1.2)^2)
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行波图
参考文献

*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