查看“︁非规范伯格斯方程”︁的源代码

'''非规范伯格斯方程 '''(Unnormalized 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,（《非线性偏微分方程手册》） SECOND EDITION p187 CRC PRESS</ref>

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

==解析解==

:<math> u(x, t) = _C3/(\beta*_C2)+2*\alpha*_C2*cot(_C1+_C2*x+_C3*t)/\beta  </math>
:<math> {u(x, t) = _C3/(\beta*_C2)+2*\alpha*_C2*coth(_C1+_C2*x+_C3*t)/\beta}  </math>
:<math> {u(x, t) = _C3/(\beta*_C2)-2*\alpha*_C2*tan(_C1+_C2*x+_C3*t)/\beta}  </math>
:<math> {u(x, t) = _C3/(\beta*_C2)+2*\alpha*_C2*tanh(_C1+_C2*x+_C3*t)/\beta}  </math>
:<math> {u(x, t) = (_C5+tanh((1/2)*_C1*(_C3+_C4*x+_C5*t-_C2)/(\alpha*_C4^2))*_C1)/(\beta*_C4)}  </math>
:<math>  {u(x, t) = (_C5+tanh((1/2)*_C1*(\sqrt(csc(_C3+_C4*x+_C5*t)-1)*\sqrt(csc(_C3+_C4*x+_C5*t)+1)*arctan(1/\sqrt(csc(_C3+_C4*x+_C5*t)^2-1))+_C2*\sqrt(csc(_C3+_C4*x+_C5*t)^2-1))/(\alpha*_C4^2*\sqrt(csc(_C3+_C4*x+_C5*t)^2-1)))*_C1)/(\beta*_C4)} </math>
:<math>  {u(x, t) = (_C5-tan((1/2)*\sqrt(2*_C1*\alpha*_C4^3*\beta-_C5^2)*(ln(cosh(_C3+_C4*x+_C5*t)+\sqrt(cosh(_C3+_C4*x+_C5*t)^2-1))+_C2)/(\alpha*_C4^2))*\sqrt(2*_C1*\alpha*_C4^3*\beta-_C5^2))/(\beta*_C4)} </math>
:<math> {u(x, t) = (_C5-tan((1/2)*\sqrt(2*_C1*\alpha*_C4^3*\beta-_C5^2)*(_C3+_C4*x+_C5*t+_C2)/(\alpha*_C4^2))*\sqrt(2*_C1*\alpha*_C4^3*\beta-_C5^2))/(\beta*_C4)}  </math>
:<math>{u(x, t) = (_C5+tanh((1/2)*\sqrt(2*_C1*\alpha*_C4^3*\beta+_C5^2)*(arctanh(1/\sqrt(1+csch(_C3+_C4*x+_C5*t)^2))-_C2)/(\alpha*_C4^2))*\sqrt(2*_C1*\alpha*_C4^3*\beta+_C5^2))/(\beta*_C4)}   </math>
:<math> {u(x, t) = (_C5-tanh((1/2)*\sqrt(2*_C1*\alpha*_C4^3*\beta+_C5^2)*((1/2)*Pi-_C3-_C4*x-_C5*t+_C2)/(\alpha*_C4^2))*\sqrt(2*_C1*\alpha*_C4^3*\beta+_C5^2))/(\beta*_C4)}  </math>
:<math> {u(x, t) = -(-_C5+tanh((1/2)*_C1*(\sqrt(sec(_C3+_C4*x+_C5*t)-1)*\sqrt(sec(_C3+_C4*x+_C5*t)+1)*arctan(1/\sqrt(sec(_C3+_C4*x+_C5*t)^2-1))+_C2*\sqrt(sec(_C3+_C4*x+_C5*t)^2-1))/(\alpha*_C4^2*\sqrt(sec(_C3+_C4*x+_C5*t)^2-1)))*_C1)/(\beta*_C4)}  </math>
:<math>  {u(x, t) = (1/2)*(\sqrt(2)*_C5+2*tanh((1/2)*\sqrt(\beta*_C1*_C4*\alpha)*(_C3+_C4*x+_C5*t+_C2)*\sqrt(2)/(_C4*\alpha))*_C4*\sqrt(\beta*_C1*_C4*\alpha))*\sqrt(2)/(\beta*_C4)} </math>

==行波图==
{|
|[[File:Unnormalized Burgers equation traveling wave plot 1.gif|thumb|非规范伯格斯方程行波图]]
|[[File:Unnormalized Burgers equation traveling wave plot 2.gif|thumb|非规范伯格斯方程行波图]]
|[[File:Unnormalized Burgers equation traveling wave plot 3.gif|thumb|非规范伯格斯方程行波图]]
|[[File:Unnormalized Burgers equation traveling wave plot 4.gif|thumb|非规范伯格斯方程行波图]]
|}
{|
|[[File:Unnormalized Burgers equation traveling wave plot 5.gif|thumb|非规范伯格斯方程行波图]]
|[[File:Unnormalized Burgers equation traveling wave plot 6.gif|thumb|非规范伯格斯方程行波图]]
|[[File:Unnormalized Burgers equation traveling wave plot 7.gif|thumb|非规范伯格斯方程行波图]]
|[[File:Unnormalized Burgers equation traveling wave plot 8.gif|thumb|非规范伯格斯方程行波图]]
|}
{|
|[[File:Unnormalized Burgers equation traveling wave plot 9.gif|thumb|非规范伯格斯方程行波图]]
|[[File:Unnormalized Burgers equation traveling wave plot 10.gif|thumb|非规范伯格斯方程行波图]]
|[[File:Unnormalized Burgers equation traveling wave plot 11.gif|thumb|非规范伯格斯方程行波图]]
|}

==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]]