查看“︁刘维方程”︁的源代码

'''刘维方程'''(Liouville equation)是一个非线性偏微分方程：<ref>李志斌编著 《非线性数学物理方程的行波解》105页 科学出版社 2008</ref>

::::::::::<math>u*u_{xt}-u*u_{x}+\alpha*u^3 = 0</math>


==解析解==
:<math>pu[2] := ln(-3.4101973587048390836*csc(1.32+1.4934776966447732662*x^1.2+1.6440433652163821333*t^1.2)^2)</math>
:<math>pu[3] := ln(-3.4101973587048390836*csch(1.32+1.4934776966447732662*x^1.2+1.6440433652163821333*t^1.2)^2)</math>
:<math>pu[4] := ln(-3.4101973587048390836*sec(1.32+1.4934776966447732662*x^1.2+1.6440433652163821333*t^1.2)^2)</math>
:<math>pu[5] := ln(3.4101973587048390836*sech(1.32+1.4934776966447732662*x^1.2+1.6440433652163821333*t^1.2)^2)</math>
:<math>pu[9] := ln(-3.4101973587048390836-3.4101973587048390836*cot(1.32+1.4934776966447732662*x^1.2+1.6440433652163821333*t^1.2)^2)</math>
:<math>pu[12] := ln(3.4101973587048390836-3.4101973587048390836*tanh(1.32+1.4934776966447732662*x^1.2+1.6440433652163821333*t^1.2)^2)</math>
:<math>pu[13] := ln(4.1031336303472692620-4.1031336303472692620*coth(1.44+1.6440433652163821333*x^1.2+1.7969454312181156991*t^1.2)^2)</math>
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==行波图==
{|
|[[File:Liouville equation traveling wave plot 1.gif|thumb|Liouville equation traveling wave plot]]
|[[File:Liouville equation traveling wave plot 2.gif|thumb|Liouville equation traveling wave plot]]
|[[File:Liouville equation traveling wave plot 3.gif|thumb|Liouville equation traveling wave plot]]
|[[File:Liouville equation traveling wave plot 4.gif|thumb|Liouville equation traveling wave plot]]
|}
{|
|[[File:Liouville equation traveling wave plot 5.gif|thumb|Liouville equation traveling wave plot]]
|[[File:Liouville equation traveling wave plot 6.gif|thumb|Liouville equation traveling wave plot]]
|[[File:Liouville equation traveling wave plot 7.gif|thumb|Liouville equation traveling wave plot]]
|[[File:Liouville equation traveling wave plot 8.gif|thumb|Liouville equation traveling wave plot]]
|}
{|
|[[File:Liouville equation traveling wave plot 9.gif|thumb|Liouville equation traveling wave plot]]
|
|}

==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

{{非线性偏微分方程}}

[[category:非线性偏微分方程]]