查看“︁MKdV方程”︁的源代码

'''mKdV方程'''是一个非线性偏微分方程：<ref>李志斌编著 《非线性数学物理方程的行波解》 页 科学出版社 2008</ref>

<math>u_{t}+6*u^2*u_{x}+u_{xxx}=0</math>

==解析解==
:<math>u(x, t) = \sqrt(6)*_C2*sech(_C1+_C2*x-_C2^3*t)</math>
:<math>u(x, t) = \sqrt(6)*_C3*JacobiDN(_C2+_C3*x+(-2*_C3^3+_C3^3*_C1^2)*t, _C1)</math>
:<math>u(x, t) = \sqrt(-6+6*_C1^2)*_C3*JacobiNC(-_C2-_C3*x-(_C3^3-2*_C3^3*_C1^2)*t, _C1)</math>
:<math>u(x, t) = \sqrt(6-6*_C1^2)*_C3*JacobiND(_C2+_C3*x+(-2*_C3^3+_C3^3*_C1^2)*t, _C1)</math>
:<math>u(x, t) = \sqrt(6)*_C1*_C3*JacobiCN(-_C2-_C3*x-(_C3^3-2*_C3^3*_C1^2)*t, _C1)</math>
:<math>u(x, t) = -I*\sqrt(6)*_C2*cot(_C1+_C2*x-2*_C2^3*t)</math>
:<math>u(x, t) = -I*\sqrt(6)*_C2*coth(_C1+_C2*x+2*_C2^3*t)</math>
:<math>u(x, t) = -I*\sqrt(6)*_C2*csc(_C1+_C2*x+_C2^3*t)</math>
:<math>u(x, t) = -I*\sqrt(6)*_C2*tanh(_C1+_C2*x+2*_C2^3*t)</math>
:<math>u(x, t) = -I*\sqrt(6)*_C2*sec(_C1+_C2*x+_C2^3*t)</math>
:<math>u(x, t) = -I*\sqrt(6)*_C2*csch(_C1+_C2*x-_C2^3*t)</math>
:<math></math>
:<math></math>
:<math></math>
:<math></math>

==行波图==
{|
|[[File:MKdV equation traveling wave plot 1.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 1.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 1.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 1.gif|thumb|mKdV equation traveling wave plot]]
|}
{|
|[[File:MKdV equation traveling wave plot 1.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 2.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 3.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 4.gif|thumb|mKdV equation traveling wave plot]]
|}
{|
|[[File:MKdV equation traveling wave plot 5.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 6.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 7.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 8.gif|thumb|mKdV equation traveling wave plot]]
|}
{|
|[[File:MKdV equation traveling wave plot 9.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 11.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 11.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 12.gif|thumb|mKdV equation traveling wave plot]]
|}
{|
|[[File:MKdV equation traveling wave plot 13.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 14.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 7.gif|thumb|mKdV equation traveling wave plot]]
|[[File:MKdV equation traveling wave plot 9.gif|thumb|mKdV 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]]