查看“︁吉本斯-查理夫方程”︁的源代码

'''吉本斯-查理夫方程'''(Gibbons-Tsarev equation)是一个非线性偏微分方程：<ref>Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p764 CRC PRESS</ref>

<math>u_{t} u_{xt}-u_{x} u_{tt}+u_{xx}+1=0</math>

==解析解==
:<math>u(x, t) = -(1/2)*x^2+_C1*x+_C2</math>
:<math>u(x, t) = exp(_c[2]*x)*_C1/_c[2]+x/_c[2]+_C2+(1/2)*_c[2]*t^2+_C3*t+_C4</math>
:<math>u(x, t) = -(1/2)*(_C3+_C1*x+_C2*t)^2/_C1^2+(_C3+_C1*x+_C2*t)*_C2+_C3</math>

==行波图==
{|
|[[File:Gibsons-Tsarev equation traveling wave plot 1.gif|thumb|Gibsons-Tsarev equation traveling wave plot]]
|[[File:Gibsons-Tsarev equation traveling wave plot 2.gif|thumb|Gibsons-Tsarev equation traveling wave plot]]
|[[File:Gibsons-Tsarev equation traveling wave plot 3.gif|thumb|Gibsons-Tsarev equation traveling wave plot]]
|[[File:Gibsons-Tsarev equation traveling wave plot 4.gif|thumb|Gibsons-Tsarev equation traveling wave plot 4]]
|}
{|
|[[File:Gibsons-Tsarev equation traveling wave plot 5.gif|thumb|Gibsons-Tsarev equation traveling wave plot 5]]
|}

==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]]