查看“︁奥斯特洛夫斯基方程”︁的源代码

'''奥斯特洛夫斯基方程'''(Ostrovsky equation)是一个模拟海洋波浪的非线性偏微分方程：<ref>Andrei D. Polyanin,Valentin F. Zaitsev,  HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p968 CRC PRESS</ref>

<math>u^2*u_{t}-u_{x}*u_{xt}+u*u_{xxt}=0</math>

==解析解==
:<math>u(x, t) = -6*_C2^2*csch(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = -6*_C2^2*sec(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = 6*_C2^2*sech(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = _C5+6*_C3^2*JacobiDN(_C2+_C3*x+_C4*t, (1/2)*sqrt((3*_C3^2+_C5)*(_C5^2+12*_C3^4+8*_C5*_C3^2))/((3*_C3^2+_C5)*_C3))^2</math>
:<math>u(x, t) = _C5-6*_C3^2*JacobiNS(_C2+_C3*x+_C4*t, (1/2)*sqrt((-3*_C3^2+_C5)*_C5*(_C5-4*_C3^2))/((-3*_C3^2+_C5)*_C3))^2</math>
:<math>u(x, t) = _C6-6*_C4^2*WeierstrassP(_C3+_C4*x+_C5*t, (1/3)*_C6^2/_C4^4, _C1)</math>
:<math>u(x, t) = _C5-(3/2)*_C5*(4*_C3^2+_C5)*JacobiND(_C2+_C3*x+_C4*t, (1/2)*sqrt((3*_C3^2+_C5)*(_C5^2+12*_C3^4+8*_C5*_C3^2))/((3*_C3^2+_C5)*_C3))^2/(3*_C3^2+_C5)</math>
:<math>u(x, t) = 2*_C2^2-6*_C2^2*coth(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = (2-4*_C1^2-2*sqrt(1-_C1^2+_C1^4))*_C3^2+(-6*_C3^2+6*_C3^2*_C1^2)*JacobiNC(_C2+_C3*x+_C4*t, _C1)^2</math>
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==行波图==
{|
|[[File:Ostrovsky equation traveling wave plot 1.gif|thumb|Ostrovsky equation traveling wave plot]]
|[[File:Ostrovsky equation traveling wave plot 2.gif|thumb|Ostrovsky equation traveling wave plot]]
|[[File:Ostrovsky equation traveling wave plot 3.gif|thumb|Ostrovsky equation traveling wave plot]]
|[[File:Ostrovsky equation traveling wave plot 4.gif|thumb|Ostrovsky equation traveling wave plot]]
|}
{|
|[[File:Ostrovsky equation traveling wave plot 5.gif|thumb|Ostrovsky equation traveling wave plot]]
|[[File:Ostrovsky equation traveling wave plot 6.gif|thumb|Ostrovsky equation traveling wave plot]]
|[[File:Ostrovsky equation traveling wave plot 7.gif|thumb|Ostrovsky equation traveling wave plot]]
|[[File:Ostrovsky equation traveling wave plot 8.gif|thumb|Ostrovsky equation traveling wave plot]]
|}
{|
|[[File:Ostrovsky equation traveling wave plot 9.gif|thumb|Ostrovsky equation traveling wave plot]]
|[[File:Ostrovsky equation traveling wave plot 10.gif|thumb|Ostrovsky equation traveling wave plot]]
|[[File:Ostrovsky equation traveling wave plot 11.gif|thumb|Ostrovsky equation traveling wave plot]]
|}

==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]]