查看“︁查菲 - 堙方特方程”︁的源代码

'''查菲 - 堙方特方程'''（Chaffee-Infante 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》 64页 科学出版社 2008</ref>

<math>u_{t}-u_{xx}+\lambda*(u^3-u)=0 </math>

==解析解==
:<math>u(x, t) = -1/2-(1/2*I)*cot(_C1-(1/4)*\sqrt(-2*\lambda)*x+(3/4*I)*\lambda*t)</math>
:<math>u(x, t) = -1/2-(1/2*I)*tan(_C1-(1/4)*\sqrt(-2*\lambda)*x-(3/4*I)*\lambda*t)</math>
:<math>u(x, t) = -1/2+(1/2*I)*cot(_C1+(1/4)*\sqrt(-2*\lambda)*x-(3/4*I)*\lambda*t)</math>
:<math>u(x, t) = -1/2+(1/2*I)*tan(_C1+(1/4)*\sqrt(-2*\lambda)*x+(3/4*I)*\lambda*t)</math>
:<math>u(x, t) = -1/2-(1/2)*coth(_C1-(1/4)*\sqrt(2)*\sqrt(\lambda)*x+(3/4)*\lambda*t)</math>
:<math>u(x, t) = -1/2+(1/2)*tanh(_C1-(1/4)*\sqrt(2)*\sqrt(\lambda)*x-(3/4)*\lambda*t)</math>
:<math>u(x, t) = 1/2-(1/2*I)*cot(_C1-(1/4)*\sqrt(-2*\lambda)*x-(3/4*I)*\lambda*t)</math>
:<math>u(x, t) = 1/2-(1/2*I)*tan(_C1+(1/4)*\sqrt(-2*\lambda)*x+(3/4*I)*\lambda*t)</math>
:<math>u(x, t) = 1/2-(1/2)*coth(_C1-(1/4)*\sqrt(2)*\sqrt(\lambda)*x-(3/4)*\lambda*t)</math>
:<math></math>
:<math></math>
:<math></math>
:<math></math>
:<math></math>
:<math></math>

==行波图==
{|
|[[File:Chaffee-Infante equation traveling wave plot 01.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 02.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 03.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 04.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|}
{|
|[[File:Chaffee-Infante equation traveling wave plot 05.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 06.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 07.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 08.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|}
{|
|[[File:Chaffee-Infante equation traveling wave plot 09.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 10.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 11.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 12.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|}
{|
|[[File:Chaffee-Infante equation traveling wave plot 13.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 14.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 15.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 16.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|}
{|
|[[File:Chaffee-Infante equation traveling wave plot 17.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 18.gif|thumb|Chaffe-Infante equation traveling wave plot]]
|[[File:Chaffee-Infante equation traveling wave plot 19.gif|thumb|Chaffe-Infante 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]]