查看“︁伊藤方程”︁的源代码

'''伊藤方程'''(Ito equation)是一个五阶非线性偏微分方程：<ref>李志斌编著 《非线性数学物理方程的行波解》 138页 科学出版社 2008</ref>

<math> U_{t}+((6*U^5+10*\alpha*(U^2*U_{xx}+U*U_{x}^2)+U_{xxxx})_{x}=0 </math>

==解析解==
:<math>u(x, t) = _C2*sech(_C1+_C2*x-_C2^5*t)</math>
:<math>u(x, t) = _C3*JacobiDN(-_C2-_C3*x-(-6*_C3^5-_C3^5*_C1^4+6*_C3^5*_C1^2)*t, _C1)</math>
:<math>u(x, t) = \sqrt(2)*_C3*JacobiCN(_C2+_C3*x-7*_C3^5*t, (1/2)*sqrt(2))</math>
:<math>u(x, t) = -I*_C2*cot(_C1+_C2*x-6*_C2^5*t)</math>
:<math>u(x, t) = -I*_C2*tan(_C1+_C2*x-6*_C2^5*t)</math>
:<math>u(x, t) = -I*_C3*JacobiNS(-_C2-_C3*x-(-_C3^5*_C1^4-_C3^5-4*_C3^5*_C1^2)*t, _C1)</math>
:<math>u(x, t) = I*_C2*csc(_C1+_C2*x-_C2^5*t)</math>
:<math>u(x, t) = (2*I)*_C3*JacobiND(_C2+_C3*x-28*_C3^5*t, sqrt(2))</math>
:<math>u(x, t) = -I*sqrt(2)*_C3*JacobiNC(_C2+_C3*x-7*_C3^5*t, (1/2)*sqrt(2))</math>
:<math>u(x, t) = -2*_C3*JacobiSN(_C2+_C3*x-28*_C3^5*t, I)</math>
:<math>u(x, t) = -\sqrt(1-_C1^2)*_C3*JacobiND(-_C2-_C3*x-(-6*_C3^5-_C3^5*_C1^4+6*_C3^5*_C1^2)*t, _C1)</math>

==行波图==
{|
|[[File:Ito equation traveling wave plot 1.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 2.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 3.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 4.gif|thumb|Ito equation traveling wave plot]]
|}
{|
|[[File:Ito equation traveling wave plot 5.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 6.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 7.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 8.gif|thumb|Ito equation traveling wave plot]]
|}
{|
|[[File:Ito equation traveling wave plot 9.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 10.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 11.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 12.gif|thumb|Ito equation traveling wave plot]]
|}
{|
|[[File:Ito equation traveling wave plot 13.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 14.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 15.gif|thumb|Ito equation traveling wave plot]]
|[[File:Ito equation traveling wave plot 16.gif|thumb|Ito 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]]