变形KdV-Burgers(Modified KdV-Burgers equation)是一个非线性偏微分方程：[1] u t + u x x x − α ∗ u 2 ∗ u x − β ∗ u x x = 0 {\displaystyle u_{t}+u_{xxx}-\alpha *u^{2}*u_{x}-\beta *u_{xx}=0} Remove ads解析解 u ( x , t ) = − ( 1 / 6 ) ∗ β ∗ ( 6 ) / ( α ) − ( 6 ) ∗ C 2 ∗ c o t ( C 1 + C 2 ∗ x + ( − 2 ∗ C 2 3 + ( 1 / 6 ) ∗ β 2 ∗ C 2 ) ∗ t ) / ( α ) {\displaystyle u(x,t)=-(1/6)*\beta *{\sqrt {(}}6)/{\sqrt {(}}\alpha )-{\sqrt {(}}6)*_{C}2*cot(_{C}1+_{C}2*x+(-2*_{C}2^{3}+(1/6)*\beta ^{2}*_{C}2)*t)/{\sqrt {(}}\alpha )} u ( x , t ) = − ( 1 / 6 ) ∗ β ∗ ( 6 ) / ( α ) − ( 6 ) ∗ C 2 ∗ c o t h ( C 1 + C 2 ∗ x + ( 2 ∗ C 2 3 + ( 1 / 6 ) ∗ β 2 ∗ C 2 ) ∗ t ) / ( α ) {\displaystyle u(x,t)=-(1/6)*\beta *{\sqrt {(}}6)/{\sqrt {(}}\alpha )-{\sqrt {(}}6)*_{C}2*coth(_{C}1+_{C}2*x+(2*_{C}2^{3}+(1/6)*\beta ^{2}*_{C}2)*t)/{\sqrt {(}}\alpha )} u ( x , t ) = − ( 1 / 6 ) ∗ β ∗ ( 6 ) / ( α ) + ( 6 ) ∗ C 2 ∗ t a n ( C 1 + C 2 ∗ x + ( − 2 ∗ C 2 3 + ( 1 / 6 ) ∗ β 2 ∗ C 2 ) ∗ t ) / ( α ) {\displaystyle u(x,t)=-(1/6)*\beta *{\sqrt {(}}6)/{\sqrt {(}}\alpha )+{\sqrt {(}}6)*_{C}2*tan(_{C}1+_{C}2*x+(-2*_{C}2^{3}+(1/6)*\beta ^{2}*_{C}2)*t)/{\sqrt {(}}\alpha )} u ( x , t ) = − ( 1 / 6 ) ∗ β ∗ ( 6 ) / ( α ) − ( 6 ) ∗ C 2 ∗ t a n h ( C 1 + C 2 ∗ x + ( 2 ∗ C 2 3 + ( 1 / 6 ) ∗ β 2 ∗ C 2 ) ∗ t ) / ( α ) {\displaystyle u(x,t)=-(1/6)*\beta *{\sqrt {(}}6)/{\sqrt {(}}\alpha )-{\sqrt {(}}6)*_{C}2*tanh(_{C}1+_{C}2*x+(2*_{C}2^{3}+(1/6)*\beta ^{2}*_{C}2)*t)/{\sqrt {(}}\alpha )} u ( x , t ) = ( 1 / 6 ) ∗ β ∗ ( 6 ) / ( α ) + ( 6 ) ∗ C 2 ∗ c o t ( C 1 + C 2 ∗ x + ( − 2 ∗ C 2 3 + ( 1 / 6 ) ∗ β 2 ∗ C 2 ) ∗ t ) / ( α ) {\displaystyle u(x,t)=(1/6)*\beta *{\sqrt {(}}6)/{\sqrt {(}}\alpha )+{\sqrt {(}}6)*_{C}2*cot(_{C}1+_{C}2*x+(-2*_{C}2^{3}+(1/6)*\beta ^{2}*_{C}2)*t)/{\sqrt {(}}\alpha )} u ( x , t ) = ( 1 / 6 ) ∗ β ∗ ( 6 ) / ( α ) + ( 6 ) ∗ C 2 ∗ c o t h ( C 1 + C 2 ∗ x + ( 2 ∗ C 2 3 + ( 1 / 6 ) ∗ β 2 ∗ C 2 ) ∗ t ) / ( α ) {\displaystyle u(x,t)=(1/6)*\beta *{\sqrt {(}}6)/{\sqrt {(}}\alpha )+{\sqrt {(}}6)*_{C}2*coth(_{C}1+_{C}2*x+(2*_{C}2^{3}+(1/6)*\beta ^{2}*_{C}2)*t)/{\sqrt {(}}\alpha )} u ( x , t ) = ( 1 / 6 ) ∗ β ∗ ( 6 ) / ( α ) − ( 6 ) ∗ C 2 ∗ t a n ( C 1 + C 2 ∗ x + ( − 2 ∗ C 2 3 + ( 1 / 6 ) ∗ β 2 ∗ C 2 ) ∗ t ) / ( α ) {\displaystyle u(x,t)=(1/6)*\beta *{\sqrt {(}}6)/{\sqrt {(}}\alpha )-{\sqrt {(}}6)*_{C}2*tan(_{C}1+_{C}2*x+(-2*_{C}2^{3}+(1/6)*\beta ^{2}*_{C}2)*t)/{\sqrt {(}}\alpha )} u ( x , t ) = ( 1 / 6 ) ∗ β ∗ ( 6 ) / ( α ) + ( 6 ) ∗ C 2 ∗ t a n h ( C 1 + C 2 ∗ x + ( 2 ∗ C 2 3 + ( 1 / 6 ) ∗ β 2 ∗ C 2 ) ∗ t ) / ( α ) {\displaystyle u(x,t)=(1/6)*\beta *{\sqrt {(}}6)/{\sqrt {(}}\alpha )+{\sqrt {(}}6)*_{C}2*tanh(_{C}1+_{C}2*x+(2*_{C}2^{3}+(1/6)*\beta ^{2}*_{C}2)*t)/{\sqrt {(}}\alpha )} Remove ads行波图 参考文献Loading content...Loading related searches...Wikiwand - on Seamless Wikipedia browsing. On steroids.Remove ads
