埃斯特韦斯-曼斯菲尔德-克拉克森方程

埃斯特韦斯 - 曼斯菲尔德 - 克拉克森方程（Estevez-Mansfield-Clarkson equation）是一个非线性偏微分方程：^[1]

${\displaystyle u_{tyyy}+\beta *u_{y}*u_{yt}+\beta *u_{yy}*u_{t}+u_{tt}=0}$

U=u(x,y,t)。

解析解

${\displaystyle u(x,y,t)=_{C}5+_{C}6*(_{C}1+_{C}2*x+_{C}3*y+_{C}4*t)}$

${\displaystyle u(x,y,t)=_{C}5+6*_{C}3*cot(_{C}1+_{C}2*x+_{C}3*y+4*_{C}3^{3}*t)/\beta }$

${\displaystyle u(x,y,t)=_{C}5+6*_{C}3*coth(_{C}1+_{C}2*x+_{C}3*y-4*_{C}3^{3}*t)/\beta }$

${\displaystyle u(x,y,t)=_{C}5-6*_{C}3*tan(_{C}1+_{C}2*x+_{C}3*y+4*_{C}3^{3}*t)/\beta }$

${\displaystyle u(x,y,t)=_{C}5+6*_{C}3*tanh(_{C}1+_{C}2*x+_{C}3*y-4*_{C}3^{3}*t)/\beta }$

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行波图

Estevez-Mansfield-Clarkson equation traveling wave plot

Estevez-Mansfield-Clarkson equation traveling wave plot

Estevez-Mansfield-Clarkson equation traveling wave plot

Estevez-Mansfield-Clarkson equation traveling wave plot

Estevez-Mansfield-Clarkson equation traveling wave plot

参考文献

1. 李志斌编著 《非线性数学物理方程的行波解》 页 科学出版社 2008

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