波格雅夫連斯基-科譳普勒琛科方程

波格雅夫連斯基-科譳普勒琛科方程（Bogoyavlenski-Konoplechenko equation）是一個二元非線性偏微分方程

$u_{xt}+\alpha *u_{xxxx}+\beta *u_{xxxy}+6*\alpha *u_{xx}*u_{x}+4*\beta *u_{xy}*u_{x}+\beta *u_{xx}*u_{y}=0$

解析解

行波解

$u(x,y,t)=_{C}5+_{C}6*cos(_{C}1+_{C}2*x-(3/4)*_{C}2*y/\beta +(1/4)*_{C}2^{3}*t)$ $u(x,y,t)=_{C}5+_{C}6*sinh(_{C}1+_{C}2*x-(3/4)*_{C}2*y/\beta -(1/4)*_{C}2^{3}*t)$ $u(x,y,t)=_{C}5+_{C}7*cosh(_{C}1+_{C}2*x-(3/4)*_{C}2*y/\beta -_{C}2^{3}*t)^{2}$ $u(x,y,t)=_{C}5+6*_{C}2*(\beta *_{C}3+_{C}2)*cot(_{C}1+_{C}2*x+_{C}3*y+(4*_{C}2^{3}+4*\beta *_{C}3*_{C}2^{2})*t)/(3*_{C}2+4*\beta *_{C}3)$ $u(x,y,t)=_{C}5-(3/4)*_{C}8*cosh(_{C}1+_{C}2*x-(3/4)*_{C}2*y/\beta -(9/4)*_{C}2^{3}*t)+_{C}8*cosh(_{C}1+_{C}2*x-(3/4)*_{C}2*y/\beta -(9/4)*_{C}2^{3}*t)^{3}$ $u(x,y,t)=_{C}6-_{C}10*cosh(_{C}2+_{C}3*x-(3/4)*_{C}3*y/\beta -4*_{C}3^{3}*t)^{2}+_{C}10*cosh(_{C}2+_{C}3*x-(3/4)*_{C}3*y/\beta -4*_{C}3^{3}*t)^{4}$ $u(x,y,t)=_{C}6+(5/16)*_{C}11*cosh(_{C}2+_{C}3*x-(3/4)*_{C}3*y/\beta -(25/4)*_{C}3^{3}*t)-(5/4)*_{C}11*cosh(_{C}2+_{C}3*x-(3/4)*_{C}3*y/\beta -(25/4)*_{C}3^{3}*t)^{3}+_{C}11*cosh(_{C}2+_{C}3*x-(3/4)*_{C}3*y/\beta -(25/4)*_{C}3^{3}*t)^{5}$

行波圖

Bogoyavlenski-Konoplechenko equation traveling wave plot

Bogoyavlenski-Konoplechenko equation traveling wave plot

Bogoyavlenski-Konoplechenko equation traveling wave plot

Bogoyavlenski-Konoplechenko equation traveling wave plot

Bogoyavlenski-Konoplechenko equation traveling wave plot

Bogoyavlenski-Konoplechenko equation traveling wave plot

Bogoyavlenski-Konoplechenko equation traveling wave plot

Bogoyavlenski-Konoplechenko equation traveling wave plot

Bogoyavlenski-Konoplechenko equation traveling wave plot

參考文獻

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