查看“︁艾克豪斯方程”︁的源代码

'''艾克豪斯方程'''(Eckhaus equation)是一个模拟色散介质中长波传播的二元非线性偏微分方程组<ref>N. Taghizadeha, M. Mirzazadeha, or, 
Filiz Tascanb：The first-integral method applied to the Eckhaus equation,Applied Mathematics Letters,Volume 25, Issue 5, May 2012, Pages 798–802</ref>.


<math>u(x, y, t)_t+v(x, t)_x+1.0*u(x, y, t)*(u(x, y, t)_x) = 0</math>

<math>v(x, t)_{xt}+u(x, y, t)_{xx}*v(x, t)+2*u(x, y, t)_x*v(x, t)_x+u(x, y, t)*(v(x, t)_{xx}+u(x, y, t)_{xx}+u(x, y, t)_{xxxx}+u(x, y, t)_{yy} = 0</math>

==行波解==
Eckhaus 方程具有一批行波解：
{{Gallery
|width=250
|height=200
|align=center
|File:Eckhaus dispersion equation traveling wave plotV29.gif|
|File:Eckhaus dispersion equation traveling wave plotV2.gif|
|File:Eckhaus dispersion equation traveling wave plotV8.gif|
|File:Eckhaus dispersion equation traveling wave plotV14.gif|
|File:Eckhaus dispersion equation traveling wave plotV11.gif|
|File:Eckhaus dispersion equation traveling wave plotU7.gif|
|File:Eckhaus dispersion equation traveling wave plotU6.gif|
|File:Eckhaus dispersion equation traveling wave plotU4.gif|
|File:Eckhaus dispersion equation traveling wave plotU27.gif|
|File:Eckhaus dispersion equation traveling wave plotU24.gif|
|File:Eckhaus dispersion equation traveling wave plotU2.gif|
|File:Eckhaus dispersion equation traveling wave plotU19.gif|
|File:Eckhaus dispersion equation traveling wave plotU14.gif|
|File:Eckhaus dispersion equation traveling wave plotU11.gif|
}}



==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]]