查看“︁本杰明-小野方程”︁的源代码

'''本杰明-小野方程'''（Benjamin-Ono equation）是一个非线性偏微分方程：<ref>李志斌编著 《非线性数学物理方程的行波解》 82页 科学出版社 2008</ref>.

<math>u_{tt}+\alpha*(u^2)_{xx}-\beta*u_{xxxx}=0</math>

==解析解==
:<math>u(x, t) = (1/2)*(-_C3^2+4*\beta*_C2^4)/_C2^2+6*\beta*_C2^2*csch(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = (1/2)*(-_C3^2+4*\beta*_C2^4)/_C2^2-6*\beta*_C2^2*sech(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = -(1/2)*(4*\beta*_C2^4+_C3^2)/_C2^2+6*\beta*_C2^2*csc(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = -(1/2)*(4*\beta*_C2^4+_C3^2)/_C2^2+6*\beta*_C2^2*sec(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = (1/2)*(8*\beta*_C2^4-_C3^2)/_C2^2+6*b\eta*_C2^2*cot(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = (1/2)*(8*\beta*_C2^4-_C3^2)/_C2^2+6*b\eta*_C2^2*tan(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = -(1/2)*(8*\beta*_C2^4+_C3^2)/_C2^2+6*\beta*_C2^2*coth(_C1+_C2*x+_C3*t)^2</math>
:<math>u(x, t) = -(1/2)*(8*\beta*_C2^4+_C3^2)/_C2^2+6*\beta*_C2^2*tanh(_C1+_C2*x+_C3*t)^2</math>
:<math>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+_C3*x+_C4*t, _C1)^2</math>
:<math>u(x, t) = -(1/2)*(-8*\beta*_C3^4+4*\beta*_C3^4*_C1^2+_C4^2)/_C3^2-6*\beta*_C3^2*JacobiDN(_C2+_C3*x+_C4*t, _C1)^2</math>
:<math>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+_C3*x+_C4*t, _C1)^2</math>
:<math>u(x, t) = -(1/2)*(4*\beta*_C3^4*_C1^2+_C4^2+4*\beta*_C3^4)/_C3^2+6*\beta*_C3^2*_C1^2*JacobiSN(_C2+_C3*x+_C4*t, _C1)^2</math>
:<math>u(x, t) = (1/2)*(-4*\beta*_C3^4+8*\beta*_C3^4*_C1^2-_C4^2)/_C3^2-6*\beta*_C3^2*_C1^2*JacobiCN(_C2+_C3*x+_C4*t, _C1)^2</math>
:<math></math>
:<math></math>

==行波图==
{|
|[[File:Benjamin-Ono equation traveling wave plot 1.gif|thumb|Benjamin-Ono equation traveling wave plot]]
|[[File:Benjamin-Ono equation traveling wave plot 2.gif|thumb|Benjamin-Ono equation traveling wave plot]]
|[[File:Benjamin-Ono equation traveling wave plot 3.gif|thumb|Benjamin-Ono equation traveling wave plot]]
|[[File:Benjamin-Ono equation traveling wave plot 4.gif|thumb|Benjamin-Ono equation traveling wave plot]]
|}
{|
|
|[[File:Benjamin-Ono equation traveling wave plot 5.gif|thumb|Benjamin-Ono equation traveling wave plot]]
|[[File:Benjamin-Ono equation traveling wave plot 6.gif|thumb|Benjamin-Ono equation traveling wave plot]]
|[[File:Benjamin-Ono equation traveling wave plot 7.gif|thumb|Benjamin-Ono equation traveling wave plot]]
|[[File:Benjamin-Ono equation traveling wave plot 8.gif|thumb|Benjamin-Ono 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

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