KdV-mKdV方程是一个非线性偏微分方程：[1] u t + 6 ∗ α ∗ u ∗ u x + 6 ∗ β ∗ u 2 ∗ u x + γ ∗ U x x x = 0 {\displaystyle u_{t}+6*\alpha *u*u_{x}+6*\beta *u^{2}*u_{x}+\gamma *U_{xxx}=0} 解析解 u ( x , t ) = − 1 / ( 2 ∗ β ) − ( β ∗ γ ∗ ( − 1 + C 1 2 ) ) ∗ C 3 ∗ J a c o b i N C ( − C 2 − C 3 ∗ x + ( 1 / 2 ) ∗ C 3 ∗ ( − 2 ∗ β ∗ γ ∗ C 3 2 + 4 ∗ β ∗ C 3 2 ∗ γ ∗ C 1 2 − 3 ) ∗ t / β , C 1 ) / β {\displaystyle u(x,t)=-1/(2*\beta )-{\sqrt {(}}\beta *\gamma *(-1+_{C}1^{2}))*_{C}3*JacobiNC(-_{C}2-_{C}3*x+(1/2)*_{C}3*(-2*\beta *\gamma *_{C}3^{2}+4*\beta *_{C}3^{2}*\gamma *_{C}1^{2}-3)*t/\beta ,_{C}1)/\beta } u ( x , t ) = − 1 / ( 2 ∗ β ) + ( β ∗ γ ∗ ( − 1 + C 1 2 ) ) ∗ C 3 ∗ J a c o b i N C ( − C 2 − C 3 ∗ x + ( 1 / 2 ) ∗ C 3 ∗ ( − 2 ∗ β ∗ γ ∗ C 3 2 + 4 ∗ β ∗ C 3 2 ∗ γ ∗ C 1 2 − 3 ) ∗ t / β , C 1 ) / β {\displaystyle u(x,t)=-1/(2*\beta )+{\sqrt {(}}\beta *\gamma *(-1+_{C}1^{2}))*_{C}3*JacobiNC(-_{C}2-_{C}3*x+(1/2)*_{C}3*(-2*\beta *\gamma *_{C}3^{2}+4*\beta *_{C}3^{2}*\gamma *_{C}1^{2}-3)*t/\beta ,_{C}1)/\beta } u ( x , t ) = − 1 / ( 2 ∗ β ) − ( − β ∗ γ ∗ ( − 1 + C 1 2 ) ) ∗ C 3 ∗ J a c o b i N D ( C 2 + C 3 ∗ x + ( 1 / 2 ) ∗ C 3 ∗ ( 2 ∗ β ∗ C 3 2 ∗ γ ∗ C 1 2 − 4 ∗ β ∗ γ ∗ C 3 2 + 3 ) ∗ t / β , C 1 ) / β {\displaystyle u(x,t)=-1/(2*\beta )-{\sqrt {(}}-\beta *\gamma *(-1+_{C}1^{2}))*_{C}3*JacobiND(_{C}2+_{C}3*x+(1/2)*_{C}3*(2*\beta *_{C}3^{2}*\gamma *_{C}1^{2}-4*\beta *\gamma *_{C}3^{2}+3)*t/\beta ,_{C}1)/\beta } u ( x , t ) = − 1 / ( 2 ∗ β ) + ( − β ∗ γ ∗ ( − 1 + C 1 2 ) ) ∗ C 3 ∗ J a c o b i N D ( C 2 + C 3 ∗ x + ( 1 / 2 ) ∗ C 3 ∗ ( 2 ∗ β ∗ C 3 2 ∗ γ ∗ C 1 2 − 4 ∗ β ∗ γ ∗ C 3 2 + 3 ) ∗ t / β , C 1 ) / β {\displaystyle u(x,t)=-1/(2*\beta )+{\sqrt {(}}-\beta *\gamma *(-1+_{C}1^{2}))*_{C}3*JacobiND(_{C}2+_{C}3*x+(1/2)*_{C}3*(2*\beta *_{C}3^{2}*\gamma *_{C}1^{2}-4*\beta *\gamma *_{C}3^{2}+3)*t/\beta ,_{C}1)/\beta } u ( x , t ) = − 1 / ( 2 ∗ β ) − γ ∗ C 2 ∗ s e c h ( C 1 + C 2 ∗ x − ( 1 / 2 ) ∗ C 2 ∗ ( 2 ∗ β ∗ γ ∗ C 2 2 − 3 ) ∗ t / β ) / ( β ∗ γ ) {\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*sech(_{C}1+_{C}2*x-(1/2)*_{C}2*(2*\beta *\gamma *_{C}2^{2}-3)*t/\beta )/{\sqrt {(}}\beta *\gamma )} u ( x , t ) = − 1 / ( 2 ∗ β ) − γ ∗ C 3 ∗ J a c o b i D N ( C 2 + C 3 ∗ x + ( 1 / 2 ) ∗ C 3 ∗ ( 2 ∗ β ∗ C 3 2 ∗ γ ∗ C 1 2 − 4 ∗ β ∗ γ ∗ C 3 2 + 3 ) ∗ t / β , C 1 ) / ( β ∗ γ ) {\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}3*JacobiDN(_{C}2+_{C}3*x+(1/2)*_{C}3*(2*\beta *_{C}3^{2}*\gamma *_{C}1^{2}-4*\beta *\gamma *_{C}3^{2}+3)*t/\beta ,_{C}1)/{\sqrt {(}}\beta *\gamma )} u ( x , t ) = − 1 / ( 2 ∗ β ) − γ ∗ C 2 ∗ c o t ( C 1 + C 2 ∗ x − ( 1 / 2 ) ∗ C 2 ∗ ( 4 ∗ β ∗ γ ∗ C 2 2 − 3 ) ∗ t / β ) / ( − β ∗ γ ) {\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*cot(_{C}1+_{C}2*x-(1/2)*_{C}2*(4*\beta *\gamma *_{C}2^{2}-3)*t/\beta )/{\sqrt {(}}-\beta *\gamma )} u ( x , t ) = − 1 / ( 2 ∗ β ) − γ ∗ C 2 ∗ c o t h ( C 1 + C 2 ∗ x + ( 1 / 2 ) ∗ C 2 ∗ ( 4 ∗ β ∗ γ ∗ C 2 2 + 3 ) ∗ t / β ) / ( − β ∗ γ ) {\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*coth(_{C}1+_{C}2*x+(1/2)*_{C}2*(4*\beta *\gamma *_{C}2^{2}+3)*t/\beta )/{\sqrt {(}}-\beta *\gamma )} u ( x , t ) = − 1 / ( 2 ∗ β ) − γ ∗ C 2 ∗ c s c h ( C 1 + C 2 ∗ x − ( 1 / 2 ) ∗ C 2 ∗ ( 2 ∗ β ∗ γ ∗ C 2 2 − 3 ) ∗ t / β ) / ( − β ∗ γ ) {\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*csch(_{C}1+_{C}2*x-(1/2)*_{C}2*(2*\beta *\gamma *_{C}2^{2}-3)*t/\beta )/{\sqrt {(}}-\beta *\gamma )} u ( x , t ) = − 1 / ( 2 ∗ β ) − γ ∗ C 2 ∗ t a n ( C 1 + C 2 ∗ x − ( 1 / 2 ) ∗ C 2 ∗ ( 4 ∗ β ∗ γ ∗ C 2 2 − 3 ) ∗ t / β ) / ( − β ∗ γ ) {\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*tan(_{C}1+_{C}2*x-(1/2)*_{C}2*(4*\beta *\gamma *_{C}2^{2}-3)*t/\beta )/{\sqrt {(}}-\beta *\gamma )} u ( x , t ) = − 1 / ( 2 ∗ β ) − γ ∗ C 2 ∗ t a n h ( C 1 + C 2 ∗ x + ( 1 / 2 ) ∗ C 2 ∗ ( 4 ∗ β ∗ γ ∗ C 2 2 + 3 ) ∗ t / β ) / ( − β ∗ γ ) {\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*tanh(_{C}1+_{C}2*x+(1/2)*_{C}2*(4*\beta *\gamma *_{C}2^{2}+3)*t/\beta )/{\sqrt {(}}-\beta *\gamma )} u ( x , t ) = − 1 / ( 2 ∗ β ) − γ ∗ C 3 ∗ J a c o b i N S ( C 2 + C 3 ∗ x + ( 1 / 2 ) ∗ C 3 ∗ ( 2 ∗ β ∗ γ ∗ C 3 2 + 2 ∗ β ∗ C 3 2 ∗ γ ∗ C 1 2 + 3 ) ∗ t / β , C 1 ) / ( − β ∗ γ ) {\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}3*JacobiNS(_{C}2+_{C}3*x+(1/2)*_{C}3*(2*\beta *\gamma *_{C}3^{2}+2*\beta *_{C}3^{2}*\gamma *_{C}1^{2}+3)*t/\beta ,_{C}1)/{\sqrt {(}}-\beta *\gamma )} 行波图 Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot Kdv-mKdv equation traveling wave plot 参考文献Loading content...Loading related searches...Wikiwand - on Seamless Wikipedia browsing. On steroids.
