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[1] u x t + α ∗ u x x x x + β ∗ u x x x y + 6 ∗ α ∗ u x x ∗ u x + 4 ∗ β ∗ u x y ∗ u x + β ∗ u x x ∗ u y = 0 {\displaystyle 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} Remove ads解析解 行波解 u ( x , y , t ) = C 5 + C 6 ∗ c o s ( C 1 + C 2 ∗ x − ( 3 / 4 ) ∗ C 2 ∗ y / β + ( 1 / 4 ) ∗ C 2 3 ∗ t ) {\displaystyle 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 ∗ s i n h ( C 1 + C 2 ∗ x − ( 3 / 4 ) ∗ C 2 ∗ y / β − ( 1 / 4 ) ∗ C 2 3 ∗ t ) {\displaystyle 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 ∗ c o s h ( C 1 + C 2 ∗ x − ( 3 / 4 ) ∗ C 2 ∗ y / β − C 2 3 ∗ t ) 2 {\displaystyle 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 ∗ ( β ∗ C 3 + C 2 ) ∗ c o t ( C 1 + C 2 ∗ x + C 3 ∗ y + ( 4 ∗ C 2 3 + 4 ∗ β ∗ C 3 ∗ C 2 2 ) ∗ t ) / ( 3 ∗ C 2 + 4 ∗ β ∗ C 3 ) {\displaystyle 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 ∗ c o s h ( C 1 + C 2 ∗ x − ( 3 / 4 ) ∗ C 2 ∗ y / β − ( 9 / 4 ) ∗ C 2 3 ∗ t ) + C 8 ∗ c o s h ( C 1 + C 2 ∗ x − ( 3 / 4 ) ∗ C 2 ∗ y / β − ( 9 / 4 ) ∗ C 2 3 ∗ t ) 3 {\displaystyle 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 ∗ c o s h ( C 2 + C 3 ∗ x − ( 3 / 4 ) ∗ C 3 ∗ y / β − 4 ∗ C 3 3 ∗ t ) 2 + C 10 ∗ c o s h ( C 2 + C 3 ∗ x − ( 3 / 4 ) ∗ C 3 ∗ y / β − 4 ∗ C 3 3 ∗ t ) 4 {\displaystyle 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 ∗ c o s h ( C 2 + C 3 ∗ x − ( 3 / 4 ) ∗ C 3 ∗ y / β − ( 25 / 4 ) ∗ C 3 3 ∗ t ) − ( 5 / 4 ) ∗ C 11 ∗ c o s h ( C 2 + C 3 ∗ x − ( 3 / 4 ) ∗ C 3 ∗ y / β − ( 25 / 4 ) ∗ C 3 3 ∗ t ) 3 + C 11 ∗ c o s h ( C 2 + C 3 ∗ x − ( 3 / 4 ) ∗ C 3 ∗ y / β − ( 25 / 4 ) ∗ C 3 3 ∗ t ) 5 {\displaystyle 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}} Remove ads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Loading content...Loading related searches...Wikiwand - on Seamless Wikipedia browsing. On steroids.Remove ads
