查看“博欣内斯克方程”的源代码

'''博欣内斯克方程'''是一个二元非线性偏微分方程：<ref>Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential Equations p339-376 Academy Press</ref>

<math>\frac{\partial^2 u }{\partial t^2}-\frac{\partial^2 u }{\partial x^2 }-\frac{\partial^2 u^2 }{\partial^2 y^2 }+\frac{\partial^4 u }{\partial x^4}=0</math>


博欣内斯克方程有如下行波解：<ref>Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential Equations p409 Academy Press</ref>


<math>u(x,t)= (3/2*(1-c^2))*sech((1/2)*\sqrt{(1-c^2)*(x-c*t))^2}</math>
<gallery>
File:Boussinesq soliton Maple plot.gif
File:Boussinesq soliton Maple 3D plot.png
File:Boussinesq soliton Maple plot.png

</gallery>

<math>u(x,y,t) = \frac{4*k^4+\omega^2-k^2}{2*l^2}+6*k^2*\frac{\cosh(k(x+x0)+l*(y+y0)-\omega*t)^2}{l^2}</math>

<gallery>
File:Boussinesq pde 3d Maple animation.gif
</gallery>


<math>u(x,y,t) :=\frac{ (1/2)*(4*k^4*cosh(k*x+k*x0+l*y+l*y0-\omega*t)^2+\omega^2*cosh(k*x+k*x0+l*y+l*y0-\omega*t)^2-k^2*cosh(k*x+k*x0+l*y+l*y0-\omega*t)^2-12*k^4)}{/(cosh(k*x+k*x0+l*y+l*y0-\omega*t)^2*l^2)}</math>
{{Gallery
|width=250
|height=200
|align=center
|File:Boussinesq pde Maple animation2.gif|
|File:Bousinesq equation traveling wave plot 01.gif|
|File:Bousinesq equation traveling wave plot 03.gif|
|File:Bousinesq equation traveling wave plot 02.gif|
|File:Bousinesq equation traveling wave plot 04.gif|
|File:Bousinesq equation traveling wave plot 06.gif|
|File:Bousinesq equation traveling wave plot 07.gif|
|File:Bousinesq equation traveling wave plot 08.gif|
}}
==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
# 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]]
[[Category:孤立子]]