查看“︁稳定跨音速气流方程”︁的源代码

'''稳定跨音速气流方程'''（Steady transonic gas flow 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 p657 CRC PRESS</ref>

<math>\alpha*u_{x}*u_{xx}+u_{yy}=0</math>

==解析解==
:<math>u(x, y) = _C4+_C5*(_C1+_C2*x+_C3*y)</math>
:<math>u(x,y)=(_C4*(C1*x+C3)+C5*y+C6)*C1^3/C2^2</math>
:<math>u(x,y)=C1*x*y+C2*x+C3*y+C4</math>
:<math>u(x,y)=((x+C2)/(y+C1))^(3/2)-(y+C4)^4+C3*y+C5</math>
:<math>u(x,y)=(y+C1)^7+4*(x+C2)^(3/2)*(y+C1)^(5/2)-(x+C2)^3/(y+C1)^2+C3*y+C4</math>

==行波图==
{|
|[[File:Steady Transonic gas flow equation traveling wave plot 2.gif|thumb|]]
|[[File:Steady Transonic gas flow equation traveling wave plot 5.gif|thumb|]]
|[[File:Steady Transonic gas flow equation traveling wave plot 9.gif|thumb|]]
|[[File:Steady Transonic gas flow equation traveling wave plot 10.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

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[[category:非线性偏微分方程]]