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：

u^2u_{t}-u_{x}u_{xt}+u*u_{xxt}=0

解析解
:u(x, t) = -6_C2^2csch(_C1+_C2x+_C3t)^2
:u(x, t) = -6_C2^2sec(_C1+_C2x+_C3t)^2
:u(x, t) = 6_C2^2sech(_C1+_C2x+_C3t)^2
:u(x, t) = _C5+6_C3^2JacobiDN(_C2+_C3x+_C4t, (1/2)sqrt((3_C3^2+_C5)(_C5^2+12_C3^4+8_C5_C3^2))/((3_C3^2+_C5)_C3))^2
:u(x, t) = _C5-6_C3^2JacobiNS(_C2+_C3x+_C4t, (1/2)sqrt((-3_C3^2+_C5)_C5(_C5-4_C3^2))/((-3_C3^2+_C5)*_C3))^2
:u(x, t) = _C6-6_C4^2WeierstrassP(_C3+_C4x+_C5t, (1/3)*_C6^2/_C4^4, _C1)
:u(x, t) = _C5-(3/2)_C5(4_C3^2+_C5)JacobiND(_C2+_C3x+_C4t, (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)
:u(x, t) = 2_C2^2-6_C2^2coth(_C1+_C2x+_C3*t)^2
:u(x, t) = (2-4_C1^2-2sqrt(1-_C1^2+_C1^4))_C3^2+(-6_C3^2+6_C3^2_C1^2)JacobiNC(_C2+_C3x+_C4*t, _C1)^2
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行波图
参考文献

*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