色散長波方程組

色散長波方程組 ((2+1)D dispersive long wave equation)是一個二元非線性偏微分方程組：^[1].

${\displaystyle u_{xt}+v_{xx}+0.5*(u^{2})_{xy}=0}$

${\displaystyle v_{t}+(u*v+u_{xy})_{x}=0}$

解析解

${\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-2.*_{C}3*sec(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t),v(x,t)=_{C}4*_{C}3-2.*_{C}4*_{C}3*sec(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t)^{2}}}$

${\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3+2.*_{C}3*sec(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t),v(x,t)=_{C}4*_{C}3-2.*_{C}4*_{C}3*sec(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t)^{2}}}$

${\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-1.414*_{C}3*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,.707),v(x,t)=-1.*_{C}4*_{C}3*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,.707)^{2}}}$

${\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-1.414*_{C}3*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,.707),v(x,t)=-1.*_{C}4*_{C}3*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,.70710678118654752440)^{2}}}$

${\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-2.*_{C}3*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,1.414),v(x,t)=-2.*_{C}4*_{C}3*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,1.414)^{2}}}$

${\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-2.*{\sqrt {(}}-1.+_{C}1^{2})*_{C}3*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1),v(x,t)=-2.*_{C}4*_{C}3+_{C}4*_{C}3*_{C}1^{2}+(2.*_{C}4*_{C}3-2.*_{C}4*_{C}3*_{C}1^{2})*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1)^{2}}}$

${\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-2.*{\sqrt {(}}-1.+_{C}1^{2})*_{C}3*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1),v(x,t)=-2.*_{C}4*_{C}3+_{C}4*_{C}3*_{C}1^{2}+(2.*_{C}4*_{C}3-2.*_{C}4*_{C}3*_{C}1^{2})*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1)^{2}}}$

${\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3+2.*{\sqrt {(}}-1.*_{C}1^{2}+1.)*_{C}3*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1),v(x,t)=-2.*_{C}4*_{C}3*_{C}1^{2}+_{C}4*_{C}3+(-2.*_{C}4*_{C}3+2.*_{C}4*_{C}3*_{C}1^{2})*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1)^{2}}}$

行波圖

(2+1)維色散長波方程行波圖

(2+1)維色散長波方程行波圖

(2+1)維色散長波方程行波圖

(2+1)維色散長波方程行波圖

(2+1)維色散長波方程行波圖

(2+1)維色散長波方程行波圖

(2+1)維色散長波方程行波圖

(2+1)維色散長波方程行波圖

(2+1)維色散長波方程行波圖

(2+1)維色散長波方程行波圖

(2+1)維色散長波方程行波圖