查看“︁非规范KdV方程”︁的源代码

'''非规范KdV方程'''（Unnormalized 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, SECOND EDITION p540-542 CRC PRESS</ref>

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

==解析解==
:<math>u(x, t) = -_C5/(\beta*_C4)-12*\alpha*_C4^2*WeierstrassP(_C3+_C4*x+_C5*t, _C2, _C1)/\beta</math>
:<math>u(x, t) = (4*\alpha*_C2^3-_C3)/(\beta*_C2)-12*\alpha*_C2^2*csc(_C1+_C2*x+_C3*t)^2/\beta</math>
:<math>u(x, t) = (4*\alpha*_C2^3-_C3)/(\beta*_C2)-12*\alpha*_C2^2*sec(_C1+_C2*x+_C3*t)^2/\beta</math>
:<math>u(x, t) = -(4*\alpha*_C2^3+_C3)/(\beta*_C2)-12*\alpha*_C2^2*csch(_C1+_C2*x+_C3*t)^2/\beta</math>
:<math>u(x, t) = -(4*\alpha*_C2^3+_C3)/(\beta*_C2)+12*\alpha*_C2^2*sech(_C1+_C2*x+_C3*t)^2/\beta</math>
:<math>u(x, t) = (8*\alpha*_C2^3-_C3)/(\beta*_C2)-12*\alpha*_C2^2*coth(_C1+_C2*x+_C3*t)^2/\beta</math>
:<math>u(x, t) = (8*\alpha*_C2^3-_C3)/(\beta*_C2)-12*\alpha*_C2^2*tanh(_C1+_C2*x+_C3*t)^2/\beta</math>
:<math>u(x, t) = (-8*\alpha*_C3^3+4*\alpha*_C3^3*_C1^2-_C4)/(\beta*_C3)+12*\alpha*_C3^2*JacobiDN(_C2+_C3*x+_C4*t, _C1)^2/\beta</math>
:<math>u(x, t) = (-8*\alpha*_C3^3+4*\alpha*_C3^3*_C1^2-_C4)/(\beta*_C3)-12*\alpha*_C3^2*(-1+_C1^2)*JacobiND(_C2+_C3*x+_C4*t, _C1)^2/\beta</math>
:<math>u(x, t) = (4*\alpha*_C3^3*_C1^2+4*\alpha*_C3^3-_C4)/(\beta*_C3)-12*\alpha*_C3^2*JacobiNS(_C2+_C3*x+_C4*t, _C1)^2/\beta</math>
:<math>u(x, t) = (4*\alpha*_C3^3*_C1^2+4*\alpha*_C3^3-_C4)/(\beta*_C3)-12*\alpha*_C3^2*_C1^2*JacobiSN(_C2+_C3*x+_C4*t, _C1)^2/\beta</math>
:<math>u(x, t) = -(8*\alpha*_C3^3*_C1^2-4*\alpha*_C3^3+_C4)/(\beta*_C3)+12*\alpha*_C3^2*_C1^2*JacobiCN(_C2+_C3*x+_C4*t, _C1)^2/\beta</math>
:<math>u(x, t) = -(8*\alpha*_C3^3*_C1^2-4*\alpha*_C3^3+_C4)/(\beta*_C3)+12*\alpha*_C3^2*(-1+_C1^2)*JacobiNC(_C2+_C3*x+_C4*t, _C1)^2/\beta</math>

==行波图==
{|
|[[File:Unnormalized KdV equation traveling wave plot 1.gif|thumb|Unnormalized KdV equation traveling wave plot]]
|[[File:Unnormalized KdV equation traveling wave plot 2.gif|thumb|Unnormalized KdV equation traveling wave plot]]
|[[File:Unnormalized KdV equation traveling wave plot 3.gif|thumb|Unnormalized KdV equation traveling wave plot]]
|[[File:Unnormalized KdV equation traveling wave plot 4.gif|thumb|Unnormalized KdV equation traveling wave plot]]
|}
{|
|[[File:Unnormalized KdV equation traveling wave plot 5.gif|thumb|Unnormalized KdV equation traveling wave plot]]
|[[File:Unnormalized KdV equation traveling wave plot 6.gif|thumb|Unnormalized KdV equation traveling wave plot]]
|[[File:Unnormalized KdV equation traveling wave plot 7.gif|thumb|Unnormalized KdV equation traveling wave plot]]
|[[File:Unnormalized KdV equation traveling wave plot 8.gif|thumb|Unnormalized KdV equation traveling wave plot]]
|}
{|
|[[File:Unnormalized KdV equation traveling wave plot 9.gif|thumb|Unnormalized KdV equation traveling wave plot]]
|[[File:Unnormalized KdV equation traveling wave plot 10.gif|thumb|Unnormalized KdV 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]]