查看“︁布罗尔-库普方程组”︁的源代码

'''布罗尔-库普方程'''（Broer-Kaup equation）是一二元个非线性偏微分方程组：<ref>阎振亚著 《复杂非线性波的构造性理论及其应用》 第65页  科学出版社 2007年</ref>

<math>u_{y,t}+(2*u*u_{x})_{x}+2*v_{xx}-u_{xxy}=0</math>

<math>v_{t}+2*(vu)_{x}+v_{xx}=0</math>

==解析解==
:<math>u(x, y, t) = -(1/2)*_C4*(2*_C3+_C2)/(_C2*(_C3+2*_C2))+_C2*cot(_C1+_C2*x+_C3*y+_C4*t), v(x, t) = -(1/4)*(2*_C2^4*_C3^3+10*_C2^5*_C3^2+16*_C2^6*_C3+8*_C2^7-_C2*_C4^2*_C3^2-_C2^2*_C4^2*_C3+_C2^3*_C4^2+_C4^2*_C3^3)/(_C2^3*(_C3^2+4*_C3*_C2+4*_C2^2))+(1/2)*_C4*(-_C3^2+_C2^2)*cot(_C1+_C2*x+_C3*y+_C4*t)/(_C2*(_C3+2*_C2))+(-(1/2)*_C3*_C2-(1/2)*_C2^2)*cot(_C1+_C2*x+_C3*y+_C4*t)^2</math>
:<math>u(x, y, t) = -(1/2)*_C4*(2*_C3+_C2)/(_C2*(_C3+2*_C2))+_C2*coth(_C1+_C2*x+_C3*y+_C4*t), v(x, t) = (1/4)*(2*_C2^4*_C3^3+10*_C2^5*_C3^2+16*_C2^6*_C3+8*_C2^7+_C2*_C4^2*_C3^2+_C2^2*_C4^2*_C3-_C2^3*_C4^2-_C4^2*_C3^3)/(_C2^3*(_C3^2+4*_C3*_C2+4*_C2^2))+(1/2)*_C4*(-_C3^2+_C2^2)*coth(_C1+_C2*x+_C3*y+_C4*t)/(_C2*(_C3+2*_C2))+(-(1/2)*_C3*_C2-(1/2)*_C2^2)*coth(_C1+_C2*x+_C3*y+_C4*t)^2</math>
:<math>u(x, y, t) = -(1/2)*_C4*(2*_C3+_C2)/(_C2*(_C3+2*_C2))-tan(_C1+_C2*x+_C3*y+_C4*t)*_C2, v(x, t) = -(1/4)*(2*_C2^4*_C3^3+10*_C2^5*_C3^2+16*_C2^6*_C3+8*_C2^7-_C2*_C4^2*_C3^2-_C2^2*_C4^2*_C3+_C2^3*_C4^2+_C4^2*_C3^3)/(_C2^3*(_C3^2+4*_C3*_C2+4*_C2^2))-(1/2)*_C4*(-_C3^2+_C2^2)*tan(_C1+_C2*x+_C3*y+_C4*t)/(_C2*(_C3+2*_C2))+(-(1/2)*_C3*_C2-(1/2)*_C2^2)*tan(_C1+_C2*x+_C3*y+_C4*t)^2</math>
:<math>u(x, y, t) = -(1/2)*_C4*(2*_C3+_C2)/(_C2*(_C3+2*_C2))+tanh(_C1+_C2*x+_C3*y+_C4*t)*_C2, v(x, t) = (1/4)*(2*_C2^4*_C3^3+10*_C2^5*_C3^2+16*_C2^6*_C3+8*_C2^7+_C2*_C4^2*_C3^2+_C2^2*_C4^2*_C3-_C2^3*_C4^2-_C4^2*_C3^3)/(_C2^3*(_C3^2+4*_C3*_C2+4*_C2^2))+(1/2)*_C4*(-_C3^2+_C2^2)*tanh(_C1+_C2*x+_C3*y+_C4*t)/(_C2*(_C3+2*_C2))+(-(1/2)*_C3*_C2-(1/2)*_C2^2)*tanh(_C1+_C2*x+_C3*y+_C4*t)^2</math>
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==行波图==
布罗尔-库普方程具有亮孤波、暗孤波和扭型孤波。
{|
|[[File:Broer-Kaup equation traveling wave plot U2.gif|thumb|Broer-Kaup equation traveling wave plot]]
|[[File:Broer-Kaup equation traveling wave plot V2.gif|thumb|Broer-Kaup equation traveling wave plot]]
|[[File:Broer-Kaup equation traveling wave plot U3.gif|thumb|Broer-Kaup equation traveling wave plot]]
|[[File:Broer-Kaup equation traveling wave plot V3.gif|thumb|Broer-Kaup equation traveling wave plot]]
|}
{|
|[[File:Broer-Kaup equation traveling wave plot U4.gif|thumb|Broer-Kaup equation traveling wave plot]]
|[[File:Broer-Kaup equation traveling wave plot V4.gif|thumb|Broer-Kaup equation traveling wave plot]]
|[[File:Broer-Kaup equation traveling wave plot U5.gif|thumb|Broer-Kaup equation traveling wave plot]]
|[[File:Broer-Kaup equation traveling wave plot V5.gif|thumb|Broer-Kaup 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
# 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]]