九阶KdV方程

九阶KdV方程(Ninth order KdV equation)是一个非线性偏微分方程：

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

其中

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

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

余类推。

解析解

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

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

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

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

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

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

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

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

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

${\displaystyle }$

${\displaystyle }$

${\displaystyle }$

${\displaystyle }$

${\displaystyle }$

${\displaystyle }$

行波图

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

参考文献

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