查看“︁别洛乌索夫-扎伯廷斯基方程”︁的源代码

'''别洛乌索夫-扎伯廷斯基方程'''（Belousov-Zhabotinsky equation)是一组模拟化学反应扩散的非线性偏微分方程<ref>李志斌编著 《非线性数学物理方程的行波解》  110-112页 科学出版社 2008</ref>：

<math> u_{t}=d*u_{xx}+u*(1-r*u-u)</math>

<math>v_{t}=v_{xx}-s*u*v</math>

==解析解==
:<math>u(x, t) = 1/(4*(1+r))-(1/2)*coth(_C1-(1/12)*\sqrt(6)*x/\sqrt(d)-(5/12)*t)/(1+r)+(1/4)*coth(_C1-(1/12)*\sqrt(6)*x/sqrt(d)-(5/12)*t)^2/(1+r)</math>
:<math>u(x, t) = 1/(4*(1+r))-(1/2)*tanh(_C1-(1/12)*\sqrt(6)*x/\sqrt(d)-(5/12)*t)/(1+r)+(1/4)*tanh(_C1-(1/12)*\sqrt(6)*x/sqrt(d)-(5/12)*t)^2/(1+r)</math>
:<math>u(x, t) = 1/(4*(1+r))-(1/2*I)*cot(_C1-(1/2)*x/\sqrt(-6*d)-(5/12*I)*t)/(1+r)-(1/4)*cot(_C1-(1/2)*x/\sqrt(-6*d)-(5/12*I)*t)^2/(1+r)</math>
:<math>u(x, t) = 1/(4*(1+r))-(1/2*I)*tan(_C1-(1/2)*x/\sqrt(-6*d)+(5/12*I)*t)/(1+r)-(1/4)*tan(_C1-(1/2)*x/\sqrt(-6*d)+(5/12*I)*t)^2/(1+r)</math>
:<math>u(x, t) = 1/(4*(1+r))-(1/2*I)*tan(_C1+(1/2)*x/\sqrt(-6*d)+(5/12*I)*t)/(1+r)-(1/4)*tan(_C1+(1/2)*x/\sqrt(-6*d)+(5/12*I)*t)^2/(1+r)</math>

==行波图==
{|
|[[File:Belousov-Zhabotinsky equation traveling wave plot 11.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 12.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 20.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 22.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|}
{|
|[[File:Belousov-Zhabotinsky equation traveling wave plot 24.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 27.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 28.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 29.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|}
{|
|[[File:Belousov-Zhabotinsky equation traveling wave plot 3.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 30.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 31.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 4.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|}
{|
|[[File:Belousov-Zhabotinsky equation traveling wave plot 5.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot34.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot33.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot32.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|}
{|
|[[File:Belousov-Zhabotinsky equation traveling wave plot 8.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 7.gif|thumb|Belousov-Zhabotinsky equation traveling wave plot]]
|[[File:Belousov-Zhabotinsky equation traveling wave plot 6.gif|thumb|Belousov-Zhabotinsky 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]]