查看“︁KdV-mKdV方程”︁的源代码

'''KdV-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》 181页 科学出版社 2008</ref>

<math>u_{t}+6*\alpha*u*u_{x}+6*\beta*u^2*u_{x}+\gamma*U_{xxx}=0</math>

==解析解==
:<math>u(x, t) = -1/(2*\beta)-\sqrt(\beta*\gamma*(-1+_C1^2))*_C3*JacobiNC(-_C2-_C3*x+(1/2)*_C3*(-2*\beta*\gamma*_C3^2+4*\beta*_C3^2*\gamma*_C1^2-3)*t/\beta, _C1)/\beta</math>
:<math>u(x, t) = -1/(2*\beta)+\sqrt(\beta*\gamma*(-1+_C1^2))*_C3*JacobiNC(-_C2-_C3*x+(1/2)*_C3*(-2*\beta*\gamma*_C3^2+4*\beta*_C3^2*\gamma*_C1^2-3)*t/\beta, _C1)/\beta</math>
:<math>u(x, t) = -1/(2*\beta)-\sqrt(-\beta*\gamma*(-1+_C1^2))*_C3*JacobiND(_C2+_C3*x+(1/2)*_C3*(2*\beta*_C3^2*\gamma*_C1^2-4*\beta*\gamma*_C3^2+3)*t/\beta, _C1)/\beta</math>
:<math>u(x, t) = -1/(2*\beta)+\sqrt(-\beta*\gamma*(-1+_C1^2))*_C3*JacobiND(_C2+_C3*x+(1/2)*_C3*(2*\beta*_C3^2*\gamma*_C1^2-4*\beta*\gamma*_C3^2+3)*t/\beta, _C1)/\beta</math>

:<math>u(x, t) = -1/(2*\beta)-\gamma*_C2*sech(_C1+_C2*x-(1/2)*_C2*(2*\beta*\gamma*_C2^2-3)*t/\beta)/\sqrt(\beta*\gamma)</math>

:<math>u(x, t) = -1/(2*\beta)-\gamma*_C3*JacobiDN(_C2+_C3*x+(1/2)*_C3*(2*\beta*_C3^2*\gamma*_C1^2-4*\beta*\gamma*_C3^2+3)*t/\beta, _C1)/\sqrt(\beta*\gamma)</math>

:<math>u(x, t) = -1/(2*\beta)-\gamma*_C2*cot(_C1+_C2*x-(1/2)*_C2*(4*\beta*\gamma*_C2^2-3)*t/\beta)/\sqrt(-\beta*\gamma)</math>

:<math>u(x, t) = -1/(2*\beta)-\gamma*_C2*coth(_C1+_C2*x+(1/2)*_C2*(4*\beta*\gamma*_C2^2+3)*t/\beta)/\sqrt(-\beta*\gamma)</math>

:<math>u(x, t) = -1/(2*\beta)-\gamma*_C2*csch(_C1+_C2*x-(1/2)*_C2*(2*\beta*\gamma*_C2^2-3)*t/\beta)/\sqrt(-\beta*\gamma)</math>

:<math>u(x, t) = -1/(2*\beta)-\gamma*_C2*tan(_C1+_C2*x-(1/2)*_C2*(4*\beta*\gamma*_C2^2-3)*t/\beta)/\sqrt(-\beta*\gamma)</math>

:<math>u(x, t) = -1/(2*\beta)-\gamma*_C2*tanh(_C1+_C2*x+(1/2)*_C2*(4*\beta*\gamma*_C2^2+3)*t/\beta)/\sqrt(-\beta*\gamma)</math>

:<math>u(x, t) = -1/(2*\beta)-\gamma*_C3*JacobiNS(_C2+_C3*x+(1/2)*_C3*(2*\beta*\gamma*_C3^2+2*\beta*_C3^2*\gamma*_C1^2+3)*t/\beta, _C1)/\sqrt(-\beta*\gamma)</math>

==行波图==
{|
|[[File:Kdv-mKdv equation traveling wave plot 1.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|[[File:Kdv-mKdv equation traveling wave plot 2.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|[[File:Kdv-mKdv equation traveling wave plot 3.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|[[File:Kdv-mKdv equation traveling wave plot 4.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|}
{|
|[[File:Kdv-mKdv equation traveling wave plot 5.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|[[File:Kdv-mKdv equation traveling wave plot 6.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|[[File:Kdv-mKdv equation traveling wave plot 7.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|[[File:Kdv-mKdv equation traveling wave plot 8.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|}
{|
|[[File:Kdv-mKdv equation traveling wave plot 9.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|[[File:Kdv-mKdv equation traveling wave plot 10.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|[[File:Kdv-mKdv equation traveling wave plot 11.gif|thumb|Kdv-mKdv equation traveling wave plot]]
|[[File:Kdv-mKdv equation traveling wave plot 12.gif|thumb|Kdv-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]]