查看“︁波格雅夫连斯基-科譳普勒琛科方程”︁的源代码

'''波格雅夫连斯基-科譳普勒琛科方程'''（Bogoyavlenski-Konoplechenko equation）是一个二元[[非线性偏微分方程]]<ref>Prabhakar, M. V.; Bhate, H.,Exact Solutions of the Bogoyavlensky-Konoplechenko Equation,Letters in Mathematical Physics;Apr2003, Vol. 64 Issue 1, p1</ref>

<math>u_{xt}+\alpha*u_{xxxx}+\beta*u_{xxxy}+6*\alpha*u_{xx}*u_{x}+4*\beta*u_{xy}*u_{x}+\beta*u_{xx}*u_{y}=0</math>

==解析解==
===行波解===
<math>u(x, y, t) = _C5+_C6*cos(_C1+_C2*x-(3/4)*_C2*y/\beta+(1/4)*_C2^3*t)</math>
<math>u(x, y, t) = _C5+_C6*sinh(_C1+_C2*x-(3/4)*_C2*y/\beta-(1/4)*_C2^3*t)</math>
<math>u(x, y, t) = _C5+_C7*cosh(_C1+_C2*x-(3/4)*_C2*y/\beta-_C2^3*t)^2</math>
<math>u(x, y, t) = _C5+6*_C2*(\beta*_C3+_C2)*cot(_C1+_C2*x+_C3*y+(4*_C2^3+4*\beta*_C3*_C2^2)*t)/(3*_C2+4*\beta*_C3)</math>
<math>u(x, y, t) = _C5-(3/4)*_C8*cosh(_C1+_C2*x-(3/4)*_C2*y/\beta-(9/4)*_C2^3*t)+_C8*cosh(_C1+_C2*x-(3/4)*_C2*y/\beta-(9/4)*_C2^3*t)^3</math>
<math>u(x, y, t) = _C6-_C10*cosh(_C2+_C3*x-(3/4)*_C3*y/\beta-4*_C3^3*t)^2+_C10*cosh(_C2+_C3*x-(3/4)*_C3*y/\beta-4*_C3^3*t)^4</math>
<math>u(x, y, t) = _C6+(5/16)*_C11*cosh(_C2+_C3*x-(3/4)*_C3*y/\beta-(25/4)*_C3^3*t)-(5/4)*_C11*cosh(_C2+_C3*x-(3/4)*_C3*y/\beta-(25/4)*_C3^3*t)^3+_C11*cosh(_C2+_C3*x-(3/4)*_C3*y/\beta-(25/4)*_C3^3*t)^5</math>
==行波图==
{|
|[[File:Bogoyavlenski-Konoplechenko equation traveling wave plot 15.gif|thumb|Bogoyavlenski-Konoplechenko equation traveling wave plot]]
|[[File:Bogoyavlenski-Konoplechenko equation traveling wave plot 16.gif|thumb|Bogoyavlenski-Konoplechenko equation traveling wave plot]]
|[[File:Bogoyavlenski-Konoplechenko equation traveling wave plot 17.gif|thumb|Bogoyavlenski-Konoplechenko equation traveling wave plot]]
|[[File:Bogoyavlenski-Konoplechenko equation traveling wave plot 20.gif|thumb|Bogoyavlenski-Konoplechenko equation traveling wave plot]]
|}
{|
|[[File:Bogoyavlenski-Konoplechenko equation traveling wave plot 27.gif|thumb|Bogoyavlenski-Konoplechenko equation traveling wave plot]]
|[[File:Bogoyavlenski-Konoplechenko equation traveling wave plot 3.gif|thumb|Bogoyavlenski-Konoplechenko equation traveling wave plot]]
|[[File:Bogoyavlenski-Konoplechenko equation traveling wave plot 4.gif|thumb|Bogoyavlenski-Konoplechenko equation traveling wave plot]]
|[[File:Bogoyavlenski-Konoplechenko equation traveling wave plot 6.gif|thumb|Bogoyavlenski-Konoplechenko equation traveling wave plot]]
|}
{|
|[[File:Bogoyavlenski-Konoplechenko equation traveling wave plot 9.gif|thumb|Bogoyavlenski-Konoplechenko 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

{{非线性偏微分方程}}

[[category:非线性偏微分方程]]