查看“︁藤田-斯托姆方程”︁的源代码

'''藤田-斯托姆方程'''(Fujita-Storm 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 p212 CRC PRESS</ref>

<math> u_{t}=a*(u^{-2}*u_{x})_{x}   </math>

==解析解==
:<math> f1 := 1/\sqrt(2*C1*x-2*a*C1^2*t+C2)  </math>
:<math> f2 := -1/\sqrt(2*C1*x-2*a*C1^2*t+C2)  </math>
:<math> f3 := 1/\sqrt((1/2)*C1*(x+C2)^2/a+C3*\exp(C1*t))  </math>
:<math>  f4 := -1/\sqrt((1/2)*C1*(x+C2)^2/a+C3*\exp(C1*t)) </math>
:<math> f5 := 1/(\sqrt(c^2*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*\sqrt(4-\exp(8*a*t)*(c*\exp(-a*t)+c^2*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))  </math>
:<math>  f6 := 1/(\sqrt(c^2*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*\sqrt(4-\exp(8*a*t)*(c*\exp(-a*t)-c^2*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t)))) </math>
:<math> f7 := -1/(\sqrt(c^2*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*\sqrt(4-\exp(8*a*t)*(c*\exp(-a*t)+c^2*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))  </math>
:<math> f8 := -1/(\sqrt(c^2*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*\sqrt(4-\exp(8*a*t)*(c*\exp(-a*t)-c^2*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t))))  </math>
:<math> f9 := 1/(\sqrt(c^2*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*\sqrt(\exp(8*a*t)*(c*\exp(-a*t)+c^2*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))  </math>
:<math>  f10 := 1/(\sqrt(c^2*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*\sqrt(\exp(8*a*t)*(c*\exp(-a*t)-c^2*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t)))) </math>
:<math>  f11 := -1/(\sqrt(c^2*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*\sqrt(\exp(8*a*t)*(c*\exp(-a*t)+c^2*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t)))) </math>
:<math> f12 := -1/(\sqrt(c^2*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*\sqrt(\exp(8*a*t)*(c*\exp(-a*t)-c^2*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t))))  </math>

==行波图==
{|
|[[File:Fujita-Storm equation plot 1.gif|thumb|藤田-斯托姆方程图]]
|[[File:Fujita-Storm equation plot 2.gif|thumb|藤田-斯托姆方程图]]
|[[File:Fujita-Storm equation plot 3.gif|thumb|藤田-斯托姆方程图]]
|[[File:Fujita-Storm equation plot 4.gif|thumb|藤田-斯托姆方程图]]
|}
{|
|[[File:Fujita-Storm equation plot 5.gif|thumb|藤田-斯托姆方程图]]
|[[File:Fujita-Storm equation plot 6.gif|thumb|藤田-斯托姆方程图]]
|[[File:Fujita-Storm equation plot 7.gif|thumb|藤田-斯托姆方程图]]
|[[File:Fujita-Storm equation plot 8.gif|thumb|藤田-斯托姆方程图]]
|}
{|
|[[File:Fujita-Storm equation plot 9.gif|thumb|藤田-斯托姆方程图]]
|[[File:Fujita-Storm equation plot 10.gif|thumb|藤田-斯托姆方程图]]
|[[File:Fujita-Storm equation plot 11.gif|thumb|藤田-斯托姆方程图]]
|[[File:Fujita-Storm equation plot 12.gif|thumb|藤田-斯托姆方程图]]
|}

==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]]