查看“︁五阶色散KdV方程”︁的源代码

''' 五阶色散KdV方程'''(Fifth order dispersion KdV equation)是一个非线性偏微分方程：<ref name=Li>李志斌 第29页</ref>。

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

==解析解==
:<math> u(x, t) = -(_C4+1008*_C3^5)/(\alpha*_C3)+3360*_C3^4*JacobiCN(_C2+_C3*x+_C4*t, I)^2/\alpha-1680*_C3^4*JacobiCN(_C2+_C3*x+_C4*t, I)^4/\alpha  </math>
:<math> u(x, t) = -(_C4+1008*_C3^5)/(\alpha*_C3)+6720*_C3^4*JacobiCN(_C2+_C3*x+_C4*t, \sqrt(2))^2/\alpha-6720*_C3^4*JacobiCN(_C2+_C3*x+_C4*t, \sqrt(2))^4/\alpha  </math>
:<math> u(x, t) = -(_C4+1008*_C3^5)/(\alpha*_C3)+3360*_C3^4*JacobiDN(_C2+_C3*x+_C4*t, I)^2/\alpha-1680*_C3^4*JacobiDN(_C2+_C3*x+_C4*t, I)^4/\alpha  </math>
:<math> u(x, t) = -(_C4+1008*_C3^5)/(\alpha*_C3)+6720*_C3^4*JacobiNC(_C2+_C3*x+_C4*t, I)^2/\alpha-6720*_C3^4*JacobiNC(_C2+_C3*x+_C4*t, I)^4/\alpha  </math>
:<math>  u(x, t) = -(_C4+1008*_C3^5)/(\alpha*_C3)+3360*_C3^4*JacobiNC(_C2+_C3*x+_C4*t, \sqrt(2))^2/\alpha-1680*_C3^4*JacobiNC(_C2+_C3*x+_C4*t, \sqrt(2))^4/\alpha </math>
:<math> u(x, t) = -(_C4+1008*_C3^5)/(\alpha*_C3)+6720*_C3^4*JacobiND(_C2+_C3*x+_C4*t, I)^2/\alpha-6720*_C3^4*JacobiND(_C2+_C3*x+_C4*t, I)^4/\alpha  </math>
:<math>  u(x, t) = -(_C4+1008*_C3^5)/(\alpha*_C3)+3360*_C3^4*JacobiNS(_C2+_C3*x+_C4*t, \sqrt(2))^2/\alpha-1680*_C3^4*JacobiNS(_C2+_C3*x+_C4*t, \sqrt(2))^4/\alpha </math>
:<math> u(x, t) = -(_C4+1008*_C3^5)/(\alpha*_C3)+6720*_C3^4*JacobiSN(_C2+_C3*x+_C4*t, \sqrt(2))^2/\alpha-6720*_C3^4*JacobiSN(_C2+_C3*x+_C4*t, \sqrt(2))^4/\alpha  </math>
:<math>  u(x, t) = -(252*_C3^5+_C4)/(\alpha*_C3)+1680*_C3^4*JacobiDN(_C2+_C3*x+_C4*t, (1/2)*\sqrt(2))^2/\alpha-1680*_C3^4*JacobiDN(_C2+_C3*x+_C4*t, (1/2)*\sqrt(2))^4/\alpha </math>
:<math> u(x, t) = -(252*_C3^5+_C4)/(\alpha*_C3)+840*_C3^4*JacobiND(_C2+_C3*x+_C4*t, (1/2)*\sqrt(2))^2/\alpha-420*_C3^4*JacobiND(_C2+_C3*x+_C4*t, (1/2)*\sqrt(2))^4/\alpha  </math>
:<math>  u(x, t) = -(252*_C3^5+_C4)/(\alpha*_C3)+1680*_C3^4*JacobiNS(_C2+_C3*x+_C4*t, (1/2)*\sqrt(2))^2/\alpha-1680*_C3^4*JacobiNS(_C2+_C3*x+_C4*t, (1/2)*\sqrt(2))^4/\alpha </math>
:<math> u(x, t) = -(252*_C3^5+_C4)/(\alpha*_C3)+840*_C3^4*JacobiSN(_C2+_C3*x+_C4*t, (1/2)*\sqrt(2))^2/\alpha-420*_C3^4*JacobiSN(_C2+_C3*x+_C4*t, (1/2)*\sqrt(2))^4/\alpha  </math>

==行波图==
{|
|[[File:Fifth order dispersion KdV equation traveling wave plot 1.gif|thumb|五阶色散KdV方程行波图]]
|[[File:Fifth order dispersion KdV equation traveling wave plot 2.gif|thumb|五阶色散KdV方程行波图]]
|[[File:Fifth order dispersion KdV equation traveling wave plot 3.gif|thumb|五阶色散KdV方程行波图]]
|[[File:Fifth order dispersion KdV equation traveling wave plot 4.gif|thumb|五阶色散KdV方程行波图]]
|}
{|
|[[File:Fifth order dispersion KdV equation traveling wave plot 5.gif|thumb|五阶色散KdV方程行波图]]
|[[File:Fifth order dispersion KdV equation traveling wave plot 6.gif|thumb|五阶色散KdV方程行波图]]
|[[File:Fifth order dispersion KdV equation traveling wave plot 7.gif|thumb|五阶色散KdV方程行波图]]
|[[File:Fifth order dispersion KdV equation traveling wave plot 8.gif|thumb|五阶色散KdV方程行波图]]
|}
{|
|[[File:Fifth order dispersion KdV equation traveling wave plot 9.gif|thumb|五阶色散KdV方程行波图]]
|[[File:Fifth order dispersion KdV equation traveling wave plot 10.gif|thumb|五阶色散KdV方程行波图]]
|[[File:Fifth order dispersion KdV equation traveling wave plot 11.gif|thumb|五阶色散KdV方程行波图]]
|[[File:Fifth order dispersion KdV equation traveling wave plot 12.gif|thumb|五阶色散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]]