本杰明-小野方程（Benjamin-Ono equation）是一个非线性偏微分方程：.

u_{tt}+\alpha(u^2)_{xx}-\betau_{xxxx}=0

解析解
:u(x, t) = (1/2)(-_C3^2+4\beta_C2^4)/_C2^2+6\beta_C2^2csch(_C1+_C2x+_C3t)^2
:u(x, t) = (1/2)(-_C3^2+4\beta_C2^4)/_C2^2-6\beta_C2^2sech(_C1+_C2x+_C3t)^2
:u(x, t) = -(1/2)(4\beta_C2^4+_C3^2)/_C2^2+6\beta_C2^2csc(_C1+_C2x+_C3t)^2
:u(x, t) = -(1/2)(4\beta_C2^4+_C3^2)/_C2^2+6\beta_C2^2sec(_C1+_C2x+_C3t)^2
:u(x, t) = (1/2)(8\beta_C2^4-_C3^2)/_C2^2+6b\eta_C2^2cot(_C1+_C2x+_C3t)^2
:u(x, t) = (1/2)(8\beta_C2^4-_C3^2)/_C2^2+6b\eta_C2^2tan(_C1+_C2x+_C3t)^2
:u(x, t) = -(1/2)(8\beta_C2^4+_C3^2)/_C2^2+6\beta_C2^2coth(_C1+_C2x+_C3t)^2
:u(x, t) = -(1/2)(8\beta_C2^4+_C3^2)/_C2^2+6\beta_C2^2tanh(_C1+_C2x+_C3t)^2
:u(x, t) = -(1/2)(-8\beta_C3^4+4\beta_C3^4_C1^2+_C4^2)/_C3^2+(-6\beta_C3^2+6\beta_C3^2_C1^2)JacobiND(_C2+_C3x+_C4t, _C1)^2
:u(x, t) = -(1/2)(-8\beta_C3^4+4\beta_C3^4_C1^2+_C4^2)/_C3^2-6\beta_C3^2JacobiDN(_C2+_C3x+_C4*t, _C1)^2
:u(x, t) = (1/2)(-4\beta_C3^4+8\beta_C3^4_C1^2-_C4^2)/_C3^2+(6\beta_C3^2-6\beta_C3^2_C1^2)JacobiNC(_C2+_C3x+_C4t, _C1)^2
:u(x, t) = -(1/2)(4\beta_C3^4_C1^2+_C4^2+4\beta_C3^4)/_C3^2+6\beta_C3^2_C1^2JacobiSN(_C2+_C3x+_C4t, _C1)^2
:u(x, t) = (1/2)(-4\beta_C3^4+8\beta_C3^4_C1^2-_C4^2)/_C3^2-6\beta_C3^2_C1^2JacobiCN(_C2+_C3x+_C4t, _C1)^2
:
:

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