查看“︁DP 方程”︁的源代码

[[File:Degasperis-Procesi equation plot.png|thumb|200px|Degasperis-Procesi equation plot]]
[[File:Degasperis-Procesi equation animation.gif|thumb|200px|Degasperis-Procesi equation animation]]
'''DP 方程'''(Degasperis-Procesi equation)是一个模拟弥散介质中非线性波动非线性偏微分方程：

 <math>\displaystyle u_t - u_{xxt} + 2\kappa u_x + 4u u_x = 3 u_x u_{xx} + u u_{xxx}</math>

==解析解==
DP方程有解析解<ref>{{Cite web |url=http://www.scholarpedia.org/article/Degasperis-Procesi_equation |title=Degasperis-Procesi equation |accessdate=2013-12-30 |archive-date=2014-01-02 |archive-url=https://web.archive.org/web/20140102214009/http://www.scholarpedia.org/article/Degasperis-Procesi_equation |dead-url=no }}</ref>


<math>A(x) := b^3+3*b^3*\frac{(\frac{(1-(1/4)*p^2)}{(1-p^2)}-1)*(\frac{(4*(1-(1/4)*p^2)}{(1-p^2)}-1)}{((2*\frac{(1-(1/4)*p^2))}{(1-p^2)}-1+\sqrt{\frac{(1-(1/4)*p^2}{(1-p^2))}}*cosh(x))}</math>


<math>B(x,t) := \frac{x}{p}+4*a^2*t+log(\frac{(\alpha+1+exp(x*(\alpha-1)))}{(alpha-1+(e)^(x* (\alpha+1)))})</math>

其中

<math>alpha := \frac{((2*a-1)*(a+1)}{((2*a+1)*(a-1)))^(1/2)}</math>

代入，

取参数p = .3, b = 1.1

<math>A(x)=1.331+\frac{.9764}{(1.148+1.036*cosh(x))}</math>


<math>B(x,t)=3.33*x+4.2967*t+ln(\frac{(5.418+exp(3.418*x))}{(3.418+exp(5.4181*x))}) </math>
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==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]]