KdV-Burgers方程

KdV-Burgers也稱Burgers-KdV方程是一個非線性偏微分方程：^[1][2]

${\displaystyle u_{t}+u*u_{x}-\alpha *u_{xx}-\beta *u_{xxx}=0}$

解析解

${\displaystyle u(x,t)=(1/25)*(-3+250*\beta ^{2}*_{C}3)/\beta +(6/25)*coth(_{C}1-(1/10)*x/\beta +_{C}3*t)/\beta +(3/25)*coth(_{C}1-(1/10)*x/\beta +_{C}3*t)^{2}/\beta }$

${\displaystyle u(x,t)=(1/25)*(-3+250*\beta ^{2}*_{C}3)/\beta +(6/25)*tanh(_{C}1-(1/10)*x/\beta +_{C}3*t)/\beta +(3/25)*tanh(_{C}1-(1/10)*x/\beta +_{C}3*t)^{2}/\beta }$

${\displaystyle u(x,t)=-(1/25)*(3+250*\beta ^{2}*_{C}3)/\beta -(6/25)*tanh(_{C}1+(1/10)*x/\beta +_{C}3*t)/\beta +(3/25)*tanh(_{C}1+(1/10)*x/\beta +_{C}3*t)^{2}/\beta }$

${\displaystyle u(x,t)=(1/25)*(-(250*I)*\beta ^{2}*_{C}3-3)/\beta -(6/25*I)*tan(_{C}1-(1/10*I)*x/\beta +_{C}3*t)/\beta -(3/25)*tan(_{C}1-(1/10*I)*x/\beta +_{C}3*t)^{2}/\beta }$

${\displaystyle u(x,t)=(1/25)*(-(250*I)*\beta ^{2}*_{C}3-3)/\beta +(6/25*I)*cot(_{C}1-(1/10*I)*x/\beta +_{C}3*t)/\beta -(3/25)*cot(_{C}1-(1/10*I)*x/\beta +_{C}3*t)^{2}/\beta }$

行波圖

KdV-Burgers equation traveling wave plot

KdV-Burgers equation traveling wave plot

KdV-Burgers equation traveling wave plot

KdV-Burgers equation traveling wave plot

KdV-Burgers equation traveling wave plot 2

KdV-Burgers equation traveling wave plot

KdV-Burgers equation traveling wave plot

KdV-Burgers equation traveling wave plot

|