查看“︁广义仓本-希伐欣斯基方程”︁的源代码

'''广义仓本-希伐欣斯基方程'''(Generalized Kuramoto-Sivashinsky 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 p983  CRC PRESS</ref>

<math>u_{t}+u^k*u_{x}+\alpha*u_{xx}+\beta*u_{xxx}+\gamma*u_{xxxx}=0</math>

==解析解==
:<math>u1 = ((3*(k+1))*(2*k+3)*\beta^3/(8*(k+3)^2*\gamma^2))^(1/k)*\exp(-\beta*z/((2*(k+3))*\gamma))*cosh(k*\beta*z/((2*(k+3))*\gamma))^(-3/k)</math>
:<math>u2 = ((k+1)*(2*k+3)*\beta^3/(72*(k+3)^2*\gamma^2))^(1/k)*(tanh(k*\beta*z1/((6*(k+3))*\gamma))-1)^(3/k)</math>

==行波图==
{|
|[[File:Generalized Kuramoto-Sivanshinsky equation traveling wave plot 1.gif|frame|行波图一]]
|[[File:Generalized Kuramoto-Sivanshinsky equation traveling wave plot 2.gif|frame|行波图二]]
|}

==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]]