查看“︁KdV-Burgers方程”︁的源代码

'''KdV-Burgers'''也称[[Burgers-KdV方程]]是一个非线性偏微分方程：<ref>{{cite journal | title = The proper analytical solution of the Korteweg-de Vries-Burgers equation | journal = Journal of Physics A-Mathematical and General | date = 1987 | first = Jian-Jun | last = Shu | volume = 20 | issue = 2 | pages = 49-56 | doi = 10.1088/0305-4470/20/2/002 }}</ref><ref>李志斌编著 《非线性数学物理方程的行波解》 61页 科学出版社 2008</ref>

<math>u_{t}+u*u_{x}-\alpha*u_{xx}-\beta*u_{xxx}=0</math>

==解析解==
:<math>u(x, t) = (1/25)*(-3+250*\beta^2*_C3)/\beta+(6/25)*coth(_C1-(1/10)*x/\beta+_C3*t)/\beta+(3/25)*coth(_C1-(1/10)*x/\beta+_C3*t)^2/\beta</math>
:<math>u(x, t) = (1/25)*(-3+250*\beta^2*_C3)/\beta+(6/25)*tanh(_C1-(1/10)*x/\beta+_C3*t)/\beta+(3/25)*tanh(_C1-(1/10)*x/\beta+_C3*t)^2/\beta</math>
:<math>u(x, t) = -(1/25)*(3+250*\beta^2*_C3)/\beta-(6/25)*tanh(_C1+(1/10)*x/\beta+_C3*t)/\beta+(3/25)*tanh(_C1+(1/10)*x/\beta+_C3*t)^2/\beta</math>
:<math>u(x, t) = (1/25)*(-(250*I)*\beta^2*_C3-3)/\beta-(6/25*I)*tan(_C1-(1/10*I)*x/\beta+_C3*t)/\beta-(3/25)*tan(_C1-(1/10*I)*x/\beta+_C3*t)^2/\beta</math>
:<math>u(x, t) = (1/25)*(-(250*I)*\beta^2*_C3-3)/\beta+(6/25*I)*cot(_C1-(1/10*I)*x/\beta+_C3*t)/\beta-(3/25)*cot(_C1-(1/10*I)*x/\beta+_C3*t)^2/\beta</math>

==行波图==
{|
|[[File:KdV-Burgers equation traveling wave plot 1.gif|thumb|KdV-Burgers equation traveling wave plot ]]
|[[File:KdV-Burgers equation traveling wave plot 2.gif|thumb|KdV-Burgers equation traveling wave plot ]]

|[[File:KdV-Burgers equation traveling wave plot 3.gif|thumb|KdV-Burgers equation traveling wave plot ]]
|[[File:KdV-Burgers equation traveling wave plot 4.gif|thumb|KdV-Burgers equation traveling wave plot ]]
|}
{|
|[[File:KdV-Burgers equation traveling wave plot 5.gif|thumb|KdV-Burgers equation traveling wave plot 2]]
|[[File:KdV-Burgers equation traveling wave plot 6.gif|thumb|KdV-Burgers equation traveling wave plot ]]
|[[File:KdV-Burgers equation traveling wave plot 7.gif|thumb|KdV-Burgers equation traveling wave plot ]]
|[[File:KdV-Burgers equation traveling wave plot 8.gif|thumb|KdV-Burgers 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]]