別洛烏索夫-扎伯廷斯基方程

別洛烏索夫-扎伯廷斯基方程（Belousov-Zhabotinsky equation)是一組模擬化學反應擴散的非線性偏微分方程^[1]：

${\displaystyle u_{t}=d*u_{xx}+u*(1-r*u-u)}$

${\displaystyle v_{t}=v_{xx}-s*u*v}$

解析解

${\displaystyle u(x,t)=1/(4*(1+r))-(1/2)*coth(_{C}1-(1/12)*{\sqrt {(}}6)*x/{\sqrt {(}}d)-(5/12)*t)/(1+r)+(1/4)*coth(_{C}1-(1/12)*{\sqrt {(}}6)*x/sqrt(d)-(5/12)*t)^{2}/(1+r)}$

${\displaystyle u(x,t)=1/(4*(1+r))-(1/2)*tanh(_{C}1-(1/12)*{\sqrt {(}}6)*x/{\sqrt {(}}d)-(5/12)*t)/(1+r)+(1/4)*tanh(_{C}1-(1/12)*{\sqrt {(}}6)*x/sqrt(d)-(5/12)*t)^{2}/(1+r)}$

${\displaystyle u(x,t)=1/(4*(1+r))-(1/2*I)*cot(_{C}1-(1/2)*x/{\sqrt {(}}-6*d)-(5/12*I)*t)/(1+r)-(1/4)*cot(_{C}1-(1/2)*x/{\sqrt {(}}-6*d)-(5/12*I)*t)^{2}/(1+r)}$

${\displaystyle u(x,t)=1/(4*(1+r))-(1/2*I)*tan(_{C}1-(1/2)*x/{\sqrt {(}}-6*d)+(5/12*I)*t)/(1+r)-(1/4)*tan(_{C}1-(1/2)*x/{\sqrt {(}}-6*d)+(5/12*I)*t)^{2}/(1+r)}$

${\displaystyle u(x,t)=1/(4*(1+r))-(1/2*I)*tan(_{C}1+(1/2)*x/{\sqrt {(}}-6*d)+(5/12*I)*t)/(1+r)-(1/4)*tan(_{C}1+(1/2)*x/{\sqrt {(}}-6*d)+(5/12*I)*t)^{2}/(1+r)}$

行波圖

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot

Belousov-Zhabotinsky equation traveling wave plot