正则长波方程

正则长波方程(Regularized long wave equation)是一个非线性偏微分方程：^[1]

$u_{t}+u_{x}+\alpha *u*u_{x}-\mu *u_{txx}=0;$

解析解

{u(x,t)=-(_{C}5+_{C}4)/(\alpha *_{C}4)+12*\mu *_{C}5*_{C}4*WeierstrassP(_{C}3+_{C}4*x+_{C}5*t,_{C}2,_{C}1)/\alpha }

{u(x,t)=(4*\mu *_{C}3*_{C}2^{2}-_{C}3-_{C}2)/(\alpha *_{C}2)+12*\mu *_{C}3*_{C}2*csch(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }

{u(x,t)=(4*\mu *_{C}3*_{C}2^{2}-_{C}3-_{C}2)/(\alpha *_{C}2)-12*\mu *_{C}3*_{C}2*sech(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }

{u(x,t)=-(4*\mu *_{C}3*_{C}2^{2}+_{C}3+_{C}2)/(\alpha *_{C}2)+12*\mu *_{C}3*_{C}2*csc(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }

{u(x,t)=(-4*\mu *_{C}4*_{C}3^{2}-_{C}4-_{C}3+8*\mu *_{C}4*_{C}3^{2}*_{C}1^{2})/(\alpha *_{C}3)-12*\mu *_{C}4*_{C}3*_{C}1^{2}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }

{u(x,t)=(-4*\mu *_{C}4*_{C}3^{2}-_{C}4-_{C}3+8*\mu *_{C}4*_{C}3^{2}*_{C}1^{2})/(\alpha *_{C}3)-12*\mu *_{C}4*_{C}3*(-1+_{C}1^{2})*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }

{u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+_{C}4+_{C}3-8*\mu *_{C}4*_{C}3^{2})/(\alpha *_{C}3)-12*\mu *_{C}4*_{C}3*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }

{u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+_{C}4+_{C}3-8*\mu *_{C}4*_{C}3^{2})/(\alpha *_{C}3)+12*\mu *_{C}4*_{C}3*(-1+_{C}1^{2})*JacobiND(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }

{u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+4*\mu *_{C}4*_{C}3^{2}+_{C}4+_{C}3)/(\alpha *_{C}3)+12*\mu *_{C}4*_{C}3*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }

{u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+4*\mu *_{C}4*_{C}3^{2}+_{C}4+_{C}3)/(\alpha *_{C}3)+12*\mu *_{C}4*_{C}3*_{C}1^{2}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }

正则长波方程行波图

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