五階色散 KdV 方程(Fifth order dispersion KdV equation) 是一個非線性偏微分方程：。

$$
u_{t}+\alpha *u*u_{x}+\beta *u_{xxx}+u_{xxxxx}=0
$$



解析解

　
: $u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -1680*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha $

　
: $u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -6720*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha $

　
: $u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -1680*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha $

　
: $u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -6720*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha $

　
: $u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha $

　
: $u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -6720*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha $

　
: $u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha $

　
: $u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -6720*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha $

　
: $u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+1680*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha $

　
: $u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+840*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -420*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha $

　
: $u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+1680*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha $

　
: $u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+840*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -420*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha $



行波圖



參考文獻

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