查看“︁查普里金方程”︁的源代码

{{noteTA
|T=zh-cn:恰普雷金方程}}
'''恰普雷金方程'''（{{lang-en|'''Chaplygin equation'''}}）是俄罗斯物理学家[[谢尔盖·阿列克谢耶维奇·恰普雷金]]在1904年发表的描写喷气流的非线性偏微分方程：<ref>Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p765  CRC PRESS</ref>

<math>0.5*u_{tt}+u_{x}*u_{xt}-u_{t}*u_{xx}=0</math>

==解析解==
:<math>u(x, t) = _C1+_C2*(_C3+C[1]*x+_C4*t)</math>
:<math>u(x, t) = _C1+((1/2)*\pi-_C3-C[1]*x-_C4*t)*_C2</math>
:<math>u(x, t) = _C1+\arctan(1/\sqrt(csc(_C3+C[1]*x+_C4*t)^2-1))*_C2</math>
:<math>u(x, t) = _C1+\ln(\cos(_C3+C[1]*x+_C4*t)+\sqrt(\cos(_C3+C[1]*x+_C4*t)^2-1))*_C</math>
:<math>u(x, t) = _C1+\ln(\cosh(_C3+C[1]*x+_C4*t)+\sqrt(\cosh(_C3+C[1]*x+_C4*t)^2-1))*_C2</math>
:<math>u(x,t)= -(0.479e-2*(11400.+581.*\tan(1.02*t)+60300.*\exp(.833*x)+3060.*exp(.833*x)*\tan(1.02*t)+79000.*\exp(1.67*x)+4010.*\exp(1.67*x)*\tan(1.02*t)))*\exp(-.833*x)/(-10.+197.*\tan(1.02*t))</math>

==行波图==
{|
|[[File:Chaplygin equation traveling wave plot 1.gif|thumb|Chaplygin equation traveling wave plot]]
|[[File:Chaplygin equation traveling wave plot 2.gif|thumb|Chaplygin equation traveling wave plot]]
|[[File:Chaplygin equation traveling wave plot 3.gif|thumb|Chaplygin equation traveling wave plot]]
|[[File:Chaplygin equation traveling wave plot 4.gif|thumb|Chaplygin equation traveling wave plot]]
|}
{|
|[[File:Chaplygin equation traveling wave plot 5.gif|thumb|Chaplygin equation traveling wave plot]]
|[[File:Chaplygin equation traveling wave plot 6.gif|thumb|Chaplygin equation traveling wave plot]]
|[[File:Chaplygin equation traveling wave plot 7.gif|thumb|Chaplygin equation traveling wave plot]]
|[[File:Chaplygin equation traveling wave plot 12a.gif|thumb|Chaplygin equation traveling wave plot]]
|}
{|
|[[File:Chaplygin equation traveling wave plot 13a.gif|thumb|Chaplygin equation traveling wave plot]]
|[[File:Chaplygin equation traveling wave plot 14a.gif|thumb|Chaplygin equation traveling wave plot]]
|}

==参考文献==
{{reflist}}

== 延伸阅读 ==
* 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]]