五阶色散KdV方程

五阶色散KdV方程(Fifth order dispersion KdV equation)是一个非线性偏微分方程：。 u t + α ∗ u ∗ u x + β ∗ u x x x + u x x x x x = 0 {\displaystyle u_{t}+\alpha *u*u_{x}+\beta *u_{xxx}+u_{xxxxx}=0} u ( x , t ) = − ( C 4 + 1008 ∗ C 3 5 ) / ( α ∗ C 3 ) + 3360 ∗ C 3 4 ∗ J a c o b i C N ( C 2 + C 3 ∗ x + C 4 ∗ t , I ) 2 / α − 1680 ∗ C 3 4 ∗ J a c o b i C N ( C 2 + C 3 ∗ x + C 4 ∗ t , I ) 4 / α {\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -1680*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha } u ( x , t ) = − ( C 4 + 1008 ∗ C 3 5 ) / ( α ∗ C 3 ) + 6720 ∗ C 3 4 ∗ J a c o b i C N ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 2 ) ) 2 / α − 6720 ∗ C 3 4 ∗ J a c o b i C N ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 2 ) ) 4 / α {\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -6720*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha } u ( x , t ) = − ( C 4 + 1008 ∗ C 3 5 ) / ( α ∗ C 3 ) + 3360 ∗ C 3 4 ∗ J a c o b i D N ( C 2 + C 3 ∗ x + C 4 ∗ t , I ) 2 / α − 1680 ∗ C 3 4 ∗ J a c o b i D N ( C 2 + C 3 ∗ x + C 4 ∗ t , I ) 4 / α {\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -1680*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha } u ( x , t ) = − ( C 4 + 1008 ∗ C 3 5 ) / ( α ∗ C 3 ) + 6720 ∗ C 3 4 ∗ J a c o b i N C ( C 2 + C 3 ∗ x + C 4 ∗ t , I ) 2 / α − 6720 ∗ C 3 4 ∗ J a c o b i N C ( C 2 + C 3 ∗ x + C 4 ∗ t , I ) 4 / α {\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -6720*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha } u ( x , t ) = − ( C 4 + 1008 ∗ C 3 5 ) / ( α ∗ C 3 ) + 3360 ∗ C 3 4 ∗ J a c o b i N C ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 2 ) ) 2 / α − 1680 ∗ C 3 4 ∗ J a c o b i N C ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 2 ) ) 4 / α {\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha } u ( x , t ) = − ( C 4 + 1008 ∗ C 3 5 ) / ( α ∗ C 3 ) + 6720 ∗ C 3 4 ∗ J a c o b i N D ( C 2 + C 3 ∗ x + C 4 ∗ t , I ) 2 / α − 6720 ∗ C 3 4 ∗ J a c o b i N D ( C 2 + C 3 ∗ x + C 4 ∗ t , I ) 4 / α {\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -6720*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha } u ( x , t ) = − ( C 4 + 1008 ∗ C 3 5 ) / ( α ∗ C 3 ) + 3360 ∗ C 3 4 ∗ J a c o b i N S ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 2 ) ) 2 / α − 1680 ∗ C 3 4 ∗ J a c o b i N S ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 2 ) ) 4 / α {\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha } u ( x , t ) = − ( C 4 + 1008 ∗ C 3 5 ) / ( α ∗ C 3 ) + 6720 ∗ C 3 4 ∗ J a c o b i S N ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 2 ) ) 2 / α − 6720 ∗ C 3 4 ∗ J a c o b i S N ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 2 ) ) 4 / α {\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -6720*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha } u ( x , t ) = − ( 252 ∗ C 3 5 + C 4 ) / ( α ∗ C 3 ) + 1680 ∗ C 3 4 ∗ J a c o b i D N ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 1 / 2 ) ∗ ( 2 ) ) 2 / α − 1680 ∗ C 3 4 ∗ J a c o b i D N ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 1 / 2 ) ∗ ( 2 ) ) 4 / α {\displaystyle u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+1680*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha } u ( x , t ) = − ( 252 ∗ C 3 5 + C 4 ) / ( α ∗ C 3 ) + 840 ∗ C 3 4 ∗ J a c o b i N D ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 1 / 2 ) ∗ ( 2 ) ) 2 / α − 420 ∗ C 3 4 ∗ J a c o b i N D ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 1 / 2 ) ∗ ( 2 ) ) 4 / α {\displaystyle u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+840*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -420*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha } u ( x , t ) = − ( 252 ∗ C 3 5 + C 4 ) / ( α ∗ C 3 ) + 1680 ∗ C 3 4 ∗ J a c o b i N S ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 1 / 2 ) ∗ ( 2 ) ) 2 / α − 1680 ∗ C 3 4 ∗ J a c o b i N S ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 1 / 2 ) ∗ ( 2 ) ) 4 / α {\displaystyle u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+1680*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha } u ( x , t ) = − ( 252 ∗ C 3 5 + C 4 ) / ( α ∗ C 3 ) + 840 ∗ C 3 4 ∗ J a c o b i S N ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 1 / 2 ) ∗ ( 2 ) ) 2 / α − 420 ∗ C 3 4 ∗ J a c o b i S N ( C 2 + C 3 ∗ x + C 4 ∗ t , ( 1 / 2 ) ∗ ( 2 ) ) 4 / α {\displaystyle u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+840*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -420*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha } 李志斌 第29页 *谷超豪 《孤立子理论中的达布变换及其几何应用》 上海科学技术出版社 *阎振亚著 《复杂非线性波的构造性理论及其应用》 科学出版社 2007年 李志斌编著 《非线性数学物理方程的行波解》 科学出版社 王东明著 《消去法及其应用》 科学出版社 2002 *何青 王丽芬编著 《Maple 教程》 科学出版社 2010 ISBN 9787030177445 Graham W. 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