查看“︁变形KdV-Burgers方程”︁的源代码

'''变形KdV-Burgers'''(Modified  KdV-Burgers 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 p1041  CRC PRESS</ref>

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

==解析解==
:<math>u(x, t) = -(1/6)*\beta*\sqrt(6)/\sqrt(\alpha)-\sqrt(6)*_C2*cot(_C1+_C2*x+(-2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)</math>
:<math>u(x, t) = -(1/6)*\beta*\sqrt(6)/\sqrt(\alpha)-\sqrt(6)*_C2*coth(_C1+_C2*x+(2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)</math>
:<math>u(x, t) = -(1/6)*\beta*\sqrt(6)/\sqrt(\alpha)+\sqrt(6)*_C2*tan(_C1+_C2*x+(-2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)</math>
:<math>u(x, t) = -(1/6)*\beta*\sqrt(6)/\sqrt(\alpha)-\sqrt(6)*_C2*tanh(_C1+_C2*x+(2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)</math>
:<math>u(x, t) = (1/6)*\beta*\sqrt(6)/\sqrt(\alpha)+\sqrt(6)*_C2*cot(_C1+_C2*x+(-2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)</math>
:<math>u(x, t) = (1/6)*\beta*\sqrt(6)/\sqrt(\alpha)+\sqrt(6)*_C2*coth(_C1+_C2*x+(2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)</math>
:<math>u(x, t) = (1/6)*\beta*\sqrt(6)/\sqrt(\alpha)-\sqrt(6)*_C2*tan(_C1+_C2*x+(-2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)</math>
:<math>u(x, t) = (1/6)*\beta*\sqrt(6)/\sqrt(\alpha)+\sqrt(6)*_C2*tanh(_C1+_C2*x+(2*_C2^3+(1/6)*\beta^2*_C2)*t)/\sqrt(\alpha)</math>

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


==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]]