查看“︁非规范变形KdV方程”︁的源代码

'''非规范变形KdV方程 '''(Unnormalized modified  KdV 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,（《非线性偏微分方程手册》） SECOND EDITION p870 CRC PRESS</ref>

<math>u_{t}+u_{xxx}+\alpha*u^2*u_{x}=0    </math>

==解析解==
:<math> {u(x, t) = \sqrt(6)*_C2*sech(_C1+_C2*x-_C2^3*t)/\sqrt(\alpha)}  </math>
:<math>  u(x, t) = \sqrt(6)*_C3*JacobiDN(_C2+_C3*x+(-2*_C3^3+_C3^3*_C1^2)*t, _C1)/\sqrt(\alpha) </math>
:<math>  u(x, t) = \sqrt(-6*\alpha*(-1+_C1^2))*_C3*JacobiND(_C2+_C3*x+(-2*_C3^3+_C3^3*_C1^2)*t, _C1)/\alpha </math>
:<math> u(x, t) = \sqrt(6)*_C1*_C3*JacobiCN(-_C2-_C3*x-(-2*_C3^3*_C1^2+_C3^3)*t, _C1)/\sqrt(\alpha)  </math>
:<math>  {u(x, t) = \sqrt(6)*\sqrt(\alpha*(-1+_C1^2))*_C3*JacobiNC(-_C2-_C3*x-(-2*_C3^3*_C1^2+_C3^3)*t, _C1)/\alpha} </math>
:<math> u(x, t) = -6*_C3*JacobiNS(_C2+_C3*x+(_C3^3*_C1^2+_C3^3)*t, _C1)/\sqrt(-6*\alpha)  </math>
:<math>  u(x, t) = -\sqrt(6)*_C3*JacobiDN(_C2+_C3*x+(-2*_C3^3+_C3^3*_C1^2)*t, _C1)/\sqrt(\alpha) </math>
:<math>   </math>

==行波图==
{|
|[[File:Unnormalized modifed KdV equation traveling wave plot 1.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 2.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 3.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 4.gif|thumb|非规范变形KdV方程行波图]]
|}
{|
|[[File:Unnormalized modifed KdV equation traveling wave plot 5.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 6.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 7.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 8.gif|thumb|非规范变形KdV方程行波图]]
|}
{|
|[[File:Unnormalized modifed KdV equation traveling wave plot 9.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 10.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 11.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 12.gif|thumb|非规范变形KdV方程行波图]]
|}
{|
|[[File:Unnormalized modifed KdV equation traveling wave plot 13.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 14.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 15.gif|thumb|非规范变形KdV方程行波图]]
|[[File:Unnormalized modifed KdV equation traveling wave plot 16.gif|thumb|非规范变形KdV方程行波图]]
|}
{|
|[[File:Unnormalized modifed KdV equation traveling wave plot 17.gif|thumb|非规范变形KdV方程行波图]]
|}

==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]]