五阶色散KdV方程

五阶色散KdV方程(Fifth order dispersion KdV equation)是一个非线性偏微分方程：^[1]。

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

解析解

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

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

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

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

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

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

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

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

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

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

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

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

行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图

五阶色散KdV方程行波图