查看“︁藏本-西瓦申斯基方程”︁的源代码

[[File:Kuramoto-Sivashinsky pde Maple 3d plot.png|thumb|right|200px|Kuramoto-Sivashinsky 偏微分方程 Maple 3d 图]]
[[File:Kuramoto-Sivashinsky pde Maple plot.png|thumb|right|200px|Kuramoto-Sivashinsky 偏微分方程 Maple 图]]
[[File:Kuramoto Sivashinsky pde Maple animation.gif|thumb|right|200px|Kuramoto Sivashinsky 偏微分方程 Maple 动画]]
'''Kuramoto-Sivashinsky 方程'''是一个非线性常微分方程<ref>Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential Equations p185-196 Academy Press</ref>：

<math>\frac{\partial u}{\partial t}=-u*\frac{\partial u}{\partial x}-\alpha*\frac{\partial^2 u }{\partial x^2}-\beta*\frac{\partial^3 u}{\partial x^3}-\gamma*\frac{\partial^4 u }{\partial x^4}</math>

此方程的解析解为

<math>u(x,t)=\frac{15*k}{19}*(11*H^3-9*H+2)</math>

其中

<math>H=tanh(\frac{1}{2}*k*x-\frac{15}{19}*k^2*t)</math>

==阿多米安近似解==
[[File:Kuramoto-Sivashinsky equation Adomian solution sin plot.gif|left|250px|]]
利用[[阿多米安分解法]]可求得Kuramoto-Sivashinsky方程的[[柯西问题]]近似解<ref>Inna Shingareve Carlos Lizarraga Celaya，Solving Nonlinear Partial Differential Equations with Maple and Mathematica p230-236, Springer</ref>。
;初始条件 u(0)=sin(x);
pa := (-.2441*sin(6.*x)+0.1693e-1*sin(4.*x)-0.5787e-4*sin(2.*x)-.5382*sin(10.*x)+.7224*sin(8.*x))*t^9+(.1514*sin(5.*x)+0.1356e-5*sin(x)+.4634*sin(9.*x)-.5585*sin(7.*x)-0.5933e-2*sin(3.*x))*t^8+(-0.8889e-1*sin(4.*x)-.4063*sin(8.*x)+0.1389e-2*sin(2.*x)+.4339*sin(6.*x))*t^7+(.3647*sin(7.*x)-.3391*sin(5.*x)-0.1085e-3*sin(x)+0.4746e-1*sin(3.*x))*t^6+(-.3375*sin(6.*x)-0.2083e-1*sin(2.*x)+.2667*sin(4.*x))*t^5+(-.2109*sin(3.*x)+0.5208e-2*sin(x)+.3255*sin(5.*x))*t^4+(-.3333*sin(4.*x)+.1667*sin(2.*x))*t^3+(-.1250*sin(x)+.3750*sin(3.*x))*t^2-.5000*t*sin(2.*x)+sin(x)

==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]]
[[category:孤立子]]