查看“︁正则长波方程”︁的源代码

''' 正则长波方程'''(Regularized long wave equation)是一个非线性偏微分方程：<ref name=gri>Griffith, chapter 13, p239-260</ref>

<math> u_{t}+u_{x}+\alpha*u*u_{x}-\mu*u_{txx}=0;   </math>

当 α=1，μ=1，正则长波方程即[[本杰明-博纳-马奥尼方程]]。

==解析解==
:<math> {u(x, t) = -(_C5+_C4)/(\alpha*_C4)+12*\mu*_C5*_C4*WeierstrassP(_C3+_C4*x+_C5*t, _C2, _C1)/\alpha}  </math>
:<math> {u(x, t) = (4*\mu*_C3*_C2^2-_C3-_C2)/(\alpha*_C2)+12*\mu*_C3*_C2*csch(_C1+_C2*x+_C3*t)^2/\alpha}  </math>
:<math>  {u(x, t) = (4*\mu*_C3*_C2^2-_C3-_C2)/(\alpha*_C2)-12*\mu*_C3*_C2*sech(_C1+_C2*x+_C3*t)^2/\alpha} </math>
:<math>  {u(x, t) = -(4*\mu*_C3*_C2^2+_C3+_C2)/(\alpha*_C2)+12*\mu*_C3*_C2*csc(_C1+_C2*x+_C3*t)^2/\alpha} </math>
:<math>  {u(x, t) = (-4*\mu*_C4*_C3^2-_C4-_C3+8*\mu*_C4*_C3^2*_C1^2)/(\alpha*_C3)-12*\mu*_C4*_C3*_C1^2*JacobiCN(_C2+_C3*x+_C4*t, _C1)^2/\alpha} </math>
:<math> {u(x, t) = (-4*\mu*_C4*_C3^2-_C4-_C3+8*\mu*_C4*_C3^2*_C1^2)/(\alpha*_C3)-12*\mu*_C4*_C3*(-1+_C1^2)*JacobiNC(_C2+_C3*x+_C4*t, _C1)^2/\alpha}  </math>
:<math> {u(x, t) = -(4*\mu*_C4*_C3^2*_C1^2+_C4+_C3-8*\mu*_C4*_C3^2)/(\alpha*_C3)-12*\mu*_C4*_C3*JacobiDN(_C2+_C3*x+_C4*t, _C1)^2/\alpha}  </math>
:<math> {u(x, t) = -(4*\mu*_C4*_C3^2*_C1^2+_C4+_C3-8*\mu*_C4*_C3^2)/(\alpha*_C3)+12*\mu*_C4*_C3*(-1+_C1^2)*JacobiND(_C2+_C3*x+_C4*t, _C1)^2/\alpha}  </math>
:<math> {u(x, t) = -(4*\mu*_C4*_C3^2*_C1^2+4*\mu*_C4*_C3^2+_C4+_C3)/(\alpha*_C3)+12*\mu*_C4*_C3*JacobiNS(_C2+_C3*x+_C4*t, _C1)^2/\alpha}  </math>
:<math> {u(x, t) = -(4*\mu*_C4*_C3^2*_C1^2+4*\mu*_C4*_C3^2+_C4+_C3)/(\alpha*_C3)+12*\mu*_C4*_C3*_C1^2*JacobiSN(_C2+_C3*x+_C4*t, _C1)^2/\alpha}  </math>

==行波图==
{|
|[[File:Regularized Long Wave equation traveling wave plot 1.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 2.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 3.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 4.gif|thumb|正则长波方程行波图]]
|}
{|
|[[File:Regularized Long Wave equation traveling wave plot 5.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 6.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 7.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 8.gif|thumb|正则长波方程行波图]]
|}
{|
|[[File:Regularized Long Wave equation traveling wave plot 9.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 10.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 11.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 12.gif|thumb|正则长波方程行波图]]
|}
{|
|[[File:Regularized Long Wave equation traveling wave plot 13.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 14.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 15.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 16.gif|thumb|正则长波方程行波图]]
|}
{|
|[[File:Regularized Long Wave equation traveling wave plot 17.gif|thumb|正则长波方程行波图]]
|[[File:Regularized Long Wave equation traveling wave plot 18.gif|thumb|正则长波方程行波图]]
|}

==参考文献==
<references/>
#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]]