查看“︁色散长波方程组”︁的源代码

'''色散长波方程组 '''((2+1)D dispersive long wave equation)是一个二元非线性偏微分方程组：<ref name=yan>阎振亚 第 62页</ref>.

<math>u_{xt}+v_{xx}+0.5*(u^2)_{xy}=0    </math>

<math>v_{t}+(u*v+u_{xy})_{x}=0    </math>

==解析解==
:<math> {u(x, y, t) = -1.*_C5/_C3-2.*_C3*sec(_C2+_C3*x+_C4*y+_C5*t), v(x, t) = _C4*_C3-2.*_C4*_C3*sec(_C2+_C3*x+_C4*y+_C5*t)^2}  </math>
:<math> {u(x, y, t) = -1.*_C5/_C3+2.*_C3*sec(_C2+_C3*x+_C4*y+_C5*t), v(x, t) = _C4*_C3-2.*_C4*_C3*sec(_C2+_C3*x+_C4*y+_C5*t)^2}  </math>
:<math> {u(x, y, t) = -1.*_C5/_C3-1.414*_C3*JacobiNC(_C2+_C3*x+_C4*y+_C5*t, .707), v(x, t) = -1.*_C4*_C3*JacobiNC(_C2+_C3*x+_C4*y+_C5*t, .707)^2}  </math>
:<math> {u(x, y, t) = -1.*_C5/_C3-1.414*_C3*JacobiNC(_C2+_C3*x+_C4*y+_C5*t, .707), v(x, t) = -1.*_C4*_C3*JacobiNC(_C2+_C3*x+_C4*y+_C5*t, .70710678118654752440)^2}  </math>
:<math> {u(x, y, t) = -1.*_C5/_C3-2.*_C3*JacobiND(_C2+_C3*x+_C4*y+_C5*t, 1.414), v(x, t) = -2.*_C4*_C3*JacobiND(_C2+_C3*x+_C4*y+_C5*t, 1.414)^2}  </math>
:<math> {u(x, y, t) = -1.*_C5/_C3-2.*\sqrt(-1.+_C1^2)*_C3*JacobiND(_C2+_C3*x+_C4*y+_C5*t, _C1), v(x, t) = -2.*_C4*_C3+_C4*_C3*_C1^2+(2.*_C4*_C3-2.*_C4*_C3*_C1^2)*JacobiND(_C2+_C3*x+_C4*y+_C5*t, _C1)^2}  </math>
:<math> {u(x, y, t) = -1.*_C5/_C3-2.*\sqrt(-1.+_C1^2)*_C3*JacobiND(_C2+_C3*x+_C4*y+_C5*t, _C1), v(x, t) = -2.*_C4*_C3+_C4*_C3*_C1^2+(2.*_C4*_C3-2.*_C4*_C3*_C1^2)*JacobiND(_C2+_C3*x+_C4*y+_C5*t, _C1)^2}  </math>
:<math> {u(x, y, t) = -1.*_C5/_C3+2.*\sqrt(-1.*_C1^2+1.)*_C3*JacobiNC(_C2+_C3*x+_C4*y+_C5*t, _C1), v(x, t) = -2.*_C4*_C3*_C1^2+_C4*_C3+(-2.*_C4*_C3+2.*_C4*_C3*_C1^2)*JacobiNC(_C2+_C3*x+_C4*y+_C5*t, _C1)^2}  </math>

==行波图==
{|
|[[File:Dispersive long wave equation traveling wave plot 1.gif|thumb|(2+1)维色散长波方程行波图]]
|[[File:Dispersive long wave equation traveling wave plot 2.gif|thumb|(2+1)维色散长波方程行波图]]
|[[File:Dispersive long wave equation traveling wave plot 3.gif|thumb|(2+1)维色散长波方程行波图]]
|[[File:Dispersive long wave equation traveling wave plot 4.gif|thumb|(2+1)维色散长波方程行波图]]
|}
{|
|[[File:Dispersive long wave equation traveling wave plot 5.gif|thumb|(2+1)维色散长波方程行波图]]
|[[File:Dispersive long wave equation traveling wave plot 6.gif|thumb|(2+1)维色散长波方程行波图]]
|[[File:Dispersive long wave equation traveling wave plot 7.gif|thumb|(2+1)维色散长波方程行波图]]
|[[File:Dispersive long wave equation traveling wave plot 8.gif|thumb|(2+1)维色散长波方程行波图]]
|}
{|
|[[File:Dispersive long wave equation traveling wave plot 9.gif|thumb|(2+1)维色散长波方程行波图]]
|[[File:Dispersive long wave equation traveling wave plot 10.gif|thumb|(2+1)维色散长波方程行波图]]
|[[File:Dispersive long wave equation traveling wave plot 11.gif|thumb|(2+1)维色散长波方程行波图]]
|}

==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]]