非规范博欣内斯克方程

非规范博欣内斯克方程（Unnormalized Boussinesq equation）是一个非线性偏微分方程： u t t − α ∗ ( u ∗ u x ) x − β ∗ u x x x x = 0 {\displaystyle u_{tt}-\alpha *(u*u_{x})_{x}-\beta *u_{xxxx}=0} u ( x , t ) = C 5 2 / ( C 4 2 ∗ α ) − 12 ∗ β ∗ C 4 2 ∗ W e i e r s t r a s s P ( C 3 + C 4 ∗ x + C 5 ∗ t , C 2 , C 1 ) / α {\displaystyle u(x,t)=_{C}5^{2}/(_{C}4^{2}*\alpha )-12*\beta *_{C}4^{2}*WeierstrassP(_{C}3+_{C}4*x+_{C}5*t,_{C}2,_{C}1)/\alpha } u ( x , t ) = − ( − C 3 2 + 4 ∗ β ∗ C 2 4 ) / ( α ∗ C 2 2 ) − 12 ∗ β ∗ C 2 2 ∗ c s c h ( C 1 + C 2 ∗ x + C 3 ∗ t ) 2 / α {\displaystyle u(x,t)=-(-_{C}3^{2}+4*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*csch(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha } u ( x , t ) = − ( − C 3 2 + 4 ∗ β ∗ C 2 4 ) / ( α ∗ C 2 2 ) + 12 ∗ β ∗ C 2 2 ∗ s e c h ( C 1 + C 2 ∗ x + C 3 ∗ t ) 2 / α {\displaystyle u(x,t)=-(-_{C}3^{2}+4*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})+12*\beta *_{C}2^{2}*sech(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha } u ( x , t ) = − ( − C 3 2 + 8 ∗ β ∗ C 2 4 ) / ( α ∗ C 2 2 ) − 12 ∗ β ∗ C 2 2 ∗ c o t ( C 1 + C 2 ∗ x + C 3 ∗ t ) 2 / α {\displaystyle u(x,t)=-(-_{C}3^{2}+8*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*cot(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha } u ( x , t ) = − ( − C 3 2 + 8 ∗ β ∗ C 2 4 ) / ( α ∗ C 2 2 ) − 12 ∗ β ∗ C 2 2 ∗ t a n ( C 1 + C 2 ∗ x + C 3 ∗ t ) 2 / α {\displaystyle u(x,t)=-(-_{C}3^{2}+8*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*tan(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha } u ( x , t ) = ( C 3 2 + 4 ∗ β ∗ C 2 4 ) / ( α ∗ C 2 2 ) − 12 ∗ β ∗ C 2 2 ∗ c s c ( C 1 + C 2 ∗ x + C 3 ∗ t ) 2 / α {\displaystyle u(x,t)=(_{C}3^{2}+4*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*csc(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha } u ( x , t ) = ( C 3 2 + 4 ∗ β ∗ C 2 4 ) / ( α ∗ C 2 2 ) − 12 ∗ β ∗ C 2 2 ∗ s e c ( C 1 + C 2 ∗ x + C 3 ∗ t ) 2 / α {\displaystyle u(x,t)=(_{C}3^{2}+4*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*sec(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha } u ( x , t ) = ( C 3 2 + 8 ∗ β ∗ C 2 4 ) / ( α ∗ C 2 2 ) − 12 ∗ β ∗ C 2 2 ∗ c o t h ( C 1 + C 2 ∗ x + C 3 ∗ t ) 2 / α {\displaystyle u(x,t)=(_{C}3^{2}+8*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*coth(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha } u ( x , t ) = ( C 3 2 + 8 ∗ β ∗ C 2 4 ) / ( α ∗ C 2 2 ) − 12 ∗ β ∗ C 2 2 ∗ t a n h ( C 1 + C 2 ∗ x + C 3 ∗ t ) 2 / α {\displaystyle u(x,t)=(_{C}3^{2}+8*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*tanh(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha } u ( x , t ) = ( − 8 ∗ β ∗ C 3 4 + C 4 2 + 4 ∗ β ∗ C 3 4 ∗ C 1 2 ) / ( α ∗ C 3 2 ) + 12 ∗ β ∗ C 3 2 ∗ J a c o b i D N ( C 2 + C 3 ∗ x + C 4 ∗ t , C 1 ) 2 / α {\displaystyle u(x,t)=(-8*\beta *_{C}3^{4}+_{C}4^{2}+4*\beta *_{C}3^{4}*_{C}1^{2})/(\alpha *_{C}3^{2})+12*\beta *_{C}3^{2}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha } u ( x , t ) = ( − 8 ∗ β ∗ C 3 4 + C 4 2 + 4 ∗ β ∗ C 3 4 ∗ C 1 2 ) / ( α ∗ C 3 2 ) − 12 ∗ β ∗ C 3 2 ∗ ( − 1 + C 1 2 ) ∗ J a c o b i N D ( C 2 + C 3 ∗ x + C 4 ∗ t , C 1 ) 2 / α {\displaystyle u(x,t)=(-8*\beta *_{C}3^{4}+_{C}4^{2}+4*\beta *_{C}3^{4}*_{C}1^{2})/(\alpha *_{C}3^{2})-12*\beta *_{C}3^{2}*(-1+_{C}1^{2})*JacobiND(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha } u ( x , t ) = ( 4 ∗ β ∗ C 3 4 ∗ C 1 2 + 4 ∗ β ∗ C 3 4 + C 4 2 ) / ( α ∗ C 3 2 ) − 12 ∗ β ∗ C 3 2 ∗ J a c o b i N S ( C 2 + C 3 ∗ x + C 4 ∗ t , C 1 ) 2 / α {\displaystyle u(x,t)=(4*\beta *_{C}3^{4}*_{C}1^{2}+4*\beta *_{C}3^{4}+_{C}4^{2})/(\alpha *_{C}3^{2})-12*\beta *_{C}3^{2}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha } u ( x , t ) = ( 4 ∗ β ∗ C 3 4 ∗ C 1 2 + 4 ∗ β ∗ C 3 4 + C 4 2 ) / ( α ∗ C 3 2 ) − 12 ∗ β ∗ C 3 2 ∗ C 1 2 ∗ J a c o b i S N ( C 2 + C 3 ∗ x + C 4 ∗ t , C 1 ) 2 / α {\displaystyle u(x,t)=(4*\beta *_{C}3^{4}*_{C}1^{2}+4*\beta *_{C}3^{4}+_{C}4^{2})/(\alpha *_{C}3^{2})-12*\beta *_{C}3^{2}*_{C}1^{2}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha } u ( x , t ) = − ( 8 ∗ β ∗ C 3 4 ∗ C 1 2 − C 4 2 − 4 ∗ β ∗ C 3 4 ) / ( α ∗ C 3 2 ) + 12 ∗ β ∗ C 3 2 ∗ C 1 2 ∗ J a c o b i C N ( C 2 + C 3 ∗ x + C 4 ∗ t , C 1 ) 2 / α {\displaystyle u(x,t)=-(8*\beta *_{C}3^{4}*_{C}1^{2}-_{C}4^{2}-4*\beta *_{C}3^{4})/(\alpha *_{C}3^{2})+12*\beta *_{C}3^{2}*_{C}1^{2}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha } u ( x , t ) = − ( 8 ∗ β ∗ C 3 4 ∗ C 1 2 − C 4 2 − 4 ∗ β ∗ C 3 4 ) / ( α ∗ C 3 2 ) + 12 ∗ β ∗ C 3 2 ∗ ( − 1 + C 1 2 ) ∗ J a c o b i N C ( C 2 + C 3 ∗ x + C 4 ∗ t , C 1 ) 2 / α {\displaystyle u(x,t)=-(8*\beta *_{C}3^{4}*_{C}1^{2}-_{C}4^{2}-4*\beta *_{C}3^{4})/(\alpha *_{C}3^{2})+12*\beta *_{C}3^{2}*(-1+_{C}1^{2})*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha } Andrei D. 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