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九階KdV方程
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九階KdV方程(Ninth order KdV equation)是一個非線性偏微分方程：[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}](http://wikimedia.org/api/rest_v1/media/math/render/svg/08fea3d3186eb3e58f29fe22573120d33c8ef270)
其中
U[t] 代表
U[x,x,x] 代表
余類推。
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解析解
![{\displaystyle w[1]:=(3816888075/22609585952)*sech(0.94052142507806327828e-5*sqrt(150156069)*(x-(11862900/3364741)*t))^{8}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/131b81ca3948fd737d01314da53e771538c8788a)
![{\displaystyle w[2]:=(3816888075/22609585952)*csch(0.94052142507806327828e-5*sqrt(150156069)*(x-(11862900/3364741)*t))^{8}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/6baec840aae0a560d52bae730fa5977146f88f08)
![{\displaystyle w[3]:=83040300/706549561+(3816888075/22609585952)*sech(0.94052142507806327828e-5*sqrt(150156069)*(x+(11862900/3364741)*t))^{8}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/e86162dbf2457419f5320f26e3e095e26425ec01)
![{\displaystyle w[4]:=83040300/706549561+(3816888075/22609585952)*csch(0.94052142507806327828e-5*sqrt(150156069)*(x+(11862900/3364741)*t))^{8}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/d10b04cba48c5e4429390ad5c4d5d51af057cf00)
![{\displaystyle w[5]:=(3816888075/22609585952)*sec(0.94052142507806327828e-5*sqrt(150156069)*(x-(11862900/3364741)*t))^{8}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/9006263cca45f0ca3b3804b43ff13d1bcebd11cc)
![{\displaystyle w[6]:=(3816888075/22609585952)*csc(0.94052142507806327828e-5*sqrt(150156069)*(x-(11862900/3364741)*t))^{8}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/ec451277230564b70a419e804dc11654cdeed56f)
![{\displaystyle w[7]:=83040300/706549561+(3816888075/22609585952)*sec(0.94052142507806327828e-5*sqrt(150156069)*(x+(11862900/3364741)*t))^{8}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/a1ff34c87cecb763e07107fd09a070199defbd35)
![{\displaystyle w[8]:=83040300/706549561+(3816888075/22609585952)*csc(0.94052142507806327828e-5*sqrt(150156069)*(x+(11862900/3364741)*t))^{8}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/db75fbe8c70dbc3e27f3197b1842dc97fc1b1c15)
![{\displaystyle w[9]:=(3816888075/22609585952)*sech(0.94052142507806327828e-5*sqrt(150156069)*(x-(11862900/3364741)*t))^{8}*(x-6*C1*t+C2)}](http://wikimedia.org/api/rest_v1/media/math/render/svg/ad33846520650d917d9518ee42a1eef0a353a0c7)
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行波圖
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參考文獻
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