九階KdV方程

九階KdV方程(Ninth order KdV equation)是一個非線性偏微分方程：

$U[t]+6*U*U[x]+U[x,x,x]-U[x,x,x,x,x]+\alpha *U[x,x,x,x,x,x,x]+\beta *U[x,x,x,x,x,x,x,x,x]=0$

其中

U[t] 代表 ${\frac {\partial u(x,t)}{\partial t}}$

U[x,x,x] 代表 ${\frac {\partial ^{3}u(x,t)}{\partial x^{3}}}$

余類推。

解析解

$w[1]:=(3816888075/22609585952)*sech(0.94052142507806327828e-5*sqrt(150156069)*(x-(11862900/3364741)*t))^{8}$

$w[2]:=(3816888075/22609585952)*csch(0.94052142507806327828e-5*sqrt(150156069)*(x-(11862900/3364741)*t))^{8}$

$w[3]:=83040300/706549561+(3816888075/22609585952)*sech(0.94052142507806327828e-5*sqrt(150156069)*(x+(11862900/3364741)*t))^{8}$

$w[4]:=83040300/706549561+(3816888075/22609585952)*csch(0.94052142507806327828e-5*sqrt(150156069)*(x+(11862900/3364741)*t))^{8}$

$w[5]:=(3816888075/22609585952)*sec(0.94052142507806327828e-5*sqrt(150156069)*(x-(11862900/3364741)*t))^{8}$

$w[6]:=(3816888075/22609585952)*csc(0.94052142507806327828e-5*sqrt(150156069)*(x-(11862900/3364741)*t))^{8}$

$w[7]:=83040300/706549561+(3816888075/22609585952)*sec(0.94052142507806327828e-5*sqrt(150156069)*(x+(11862900/3364741)*t))^{8}$

$w[8]:=83040300/706549561+(3816888075/22609585952)*csc(0.94052142507806327828e-5*sqrt(150156069)*(x+(11862900/3364741)*t))^{8}$

$w[9]:=(3816888075/22609585952)*sech(0.94052142507806327828e-5*sqrt(150156069)*(x-(11862900/3364741)*t))^{8}*(x-6*C1*t+C2)$

${\displaystyle }$

${\displaystyle }$

${\displaystyle }$

${\displaystyle }$

${\displaystyle }$

${\displaystyle }$

行波圖

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

Nineth order KdV equation traveling wave plot

參考文獻

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