九阶KdV方程(Ninth order KdV equation)是一个非线性偏微分方程：^[1]

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

其中

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

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

余类推。

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

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

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

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

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

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

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

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

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

${\displaystyle }$

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1. ^ Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p1041 CRC PRESS

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