查看“︁布雷瑟顿方程”︁的源代码

'''布雷瑟顿方程'''(Bretherton 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》 152页 科学出版社 2008</ref>

<math>u_{tt}+u_{xx}+u_{xxxx}-\alpha*u^3=0</math>

==解析解==
利用[[Maple]]软件包TWSolution可得布雷瑟顿方程两个WeirstrassP函数行波解和六个Jacobi椭圆函数行波解。

:<math>{u(x, t) = -(1/30)*(_C5^2+_C4^2)*\sqrt(30)/(\sqrt(\alpha)*_C4^2)-2*\sqrt(30)*_C4^2*WeierstrassP(_C3+_C4*x+_C5*t, -(1/180)*(_C5^4+2*_C5^2*_C4^2+_C4^4)/_C4^8, (1/5400)*(_C5^2+_C4^2)*(_C5^4+2*_C5^2*_C4^2+_C4^4)/_C4^12)/\sqrt(\alpha)}</math>
:<math>{u(x, t) = (1/30)*(_C5^2+_C4^2)*\sqrt(30)/(\sqrt(\alpha)*_C4^2)+2*\sqrt(30)*_C4^2*WeierstrassP(_C3+_C4*x+_C5*t, -(1/180)*(_C5^4+2*_C5^2*_C4^2+_C4^4)/_C4^8, (1/5400)*(_C5^2+_C4^2)*(_C5^4+2*_C5^2*_C4^2+_C4^4)/_C4^12)/\sqrt(\alpha)}</math>
:<math>p[3] := -4.4229081351691113421-0.93307517430300270455e-1*I+(18.208764436791314548+0.*I)*JacobiDN(1.22+1.3*x+(15.095721921379631782+24.271454992000839308*I)*t, 1.1984050731412980386-.42555954136146448708*I)^1.5</math>
:<math>p[4] := -5.1919544739096094160+5.3436314406870407268*I+(18.208764436791314548+0.*I)*JacobiNS(1.22+1.3*x+(15.095721921379631782+24.271454992000839308*I)*t, 1.1984050731412980386-.42555954136146448708*I)^1.5</math>
:<math>p[5] := -2.5743416547838020433-3.2877514938561477464*I+(2.3878725879366620662-40.119130323671954306*I)*JacobiND(1.22+1.3*x+(15.095721921379631782+24.271454992000839308*I)*t, 1.1984050731412980386-.42555954136146448708*I)^1.5</math>
:<math>p[6] := -5.5945307529851545322+1.6067031040792677714*I+(2.3878725879366620662-40.119130323671954306*I)*JacobiNC(1.22+1.3*x+(15.095721921379631782+24.271454992000839308*I)*t, 1.1984050731412980386-.42555954136146448708*I)^1.5</math>
:<math>p[7] := -5.1805015655073574818+2.2007257608074972052*I+(21.217747598613725681-27.288660748456732356*I)*JacobiSN(1.22+1.3*x+(15.095721921379631782+24.271454992000839308*I)*t, 1.1984050731412980386-.42555954136146448708*I)^1.5</math>
:<math>p[8] := -5.7120768471542134149-.77489365858670457610*I+(21.217747598613725681-27.288660748456732356*I)*JacobiCN(1.22+1.3*x+(15.095721921379631782+24.271454992000839308*I)*t, 1.1984050731412980386-.42555954136146448708*I)^1.5</math>
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==行波图==
{|
|[[File:Bretherton equation traveling wave WeierstrassP plot 1.gif|thumb|Bretherton equation traveling wave WeierstrassP plot 1]]
|[[File:Bretherton equation traveling wave WeierstrassP plot 2.gif|thumb|Bretherton equation traveling wave WeierstrassP plot 1]]
|[[File:Bretherton equation traveling wave Jacobi function plot 1.gif|thumb|Bretherton equation traveling wave Jacobi function plot]]
|[[File:Bretherton equation traveling wave Jacobi function plot 2.gif|thumb|Bretherton equation traveling wave Jacobi function plot]]
|}
{|
|[[File:Bretherton equation traveling wave Jacobi function plot 3.gif|thumb|Bretherton equation traveling wave Jacobi function plot]]
|[[File:Bretherton equation traveling wave Jacobi function plot 4.gif|thumb|Bretherton equation traveling wave Jacobi function plot]]
|[[File:Bretherton equation traveling wave Jacobi function plot 5.gif|thumb|Bretherton equation traveling wave Jacobi function plot]]
|[[File:Bretherton equation traveling wave Jacobi function plot 6.gif|thumb|Bretherton equation traveling wave Jacobi function 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]]