耦合KdV方程组(Coupled KdV equation)是一个二元非线性偏微分方程组:[1]
解析解
![{\displaystyle u(x,t)=(1/3)*(-_{C}3+\alpha *_{C}2^{3})/(\alpha *_{C}2)-2*_{C}2^{2}*csc(_{C}1+_{C}2*x+_{C}3*t)^{2},v(x,t)=-(1/3)*{\sqrt {(}}12*\alpha *_{C}2^{4}+6*_{C}2*_{C}3)*csc(_{C}1+_{C}2*x+_{C}3*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d9aa86fc8529eacbda20ac2768e9ecd7c5da9d2f)
![{\displaystyle u(x,t)=(1/3)*(-_{C}3+\alpha *_{C}2^{3})/(\alpha *_{C}2)-2*_{C}2^{2}*sec(_{C}1+_{C}2*x+_{C}3*t)^{2},v(x,t)=-(1/3)*{\sqrt {(}}12*\alpha *_{C}2^{4}+6*_{C}2*_{C}3)*sec(_{C}1+_{C}2*x+_{C}3*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3b06521b1837c5ca9f1ffb253cd905864a67169b)
![{\displaystyle u(x,t)=(1/3)*(-_{C}3+2*\alpha *_{C}2^{3})/(\alpha *_{C}2)-2*_{C}2^{2}*coth(_{C}1+_{C}2*x+_{C}3*t)^{2},v(x,t)=-(1/3)*{\sqrt {(}}6*_{C}2*_{C}3+24*\alpha *_{C}2^{4})*coth(_{C}1+_{C}2*x+_{C}3*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41ac381e787d5c53154d15b3bacab24a88ff95ac)
![{\displaystyle u(x,t)=(1/3)*(-_{C}3+2*\alpha *_{C}2^{3})/(alpha*_{C}2)-2*_{C}2^{2}*tanh(_{C}1+_{C}2*x+_{C}3*t)^{2},v(x,t)=-(1/3)*{\sqrt {(}}6*_{C}2*_{C}3+24*alpha*_{C}2^{4})*tanh(_{C}1+_{C}2*x+_{C}3*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5c1c0e960451758b7dad8a90b2833be7f9b5284)
![{\displaystyle u(x,t)=-(1/3)*(_{C}3+\alpha *_{C}2^{3})/(\alpha *_{C}2)-2*_{C}2^{2}*csch(_{C}1+_{C}2*x+_{C}3*t)^{2},v(x,t)=-(1/3)*{\sqrt {(}}6*_{C}2*_{C}3-12*alpha*_{C}2^{4})*csch(_{C}1+_{C}2*x+_{C}3*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f69ed550b86f3d7327a50f23aa7437507236d7f5)
![{\displaystyle u(x,t)=-(1/3)*(_{C}3+8*\alpha *_{C}2^{3})/(\alpha *_{C}2)-4*_{C}2^{2}*tan(_{C}1+_{C}2*x+_{C}3*t)^{2},v(x,t)=-(1/6)*(_{C}3+8*\alpha *_{C}2^{3})*{\sqrt {(}}2)/(_{C}2*{\sqrt {(}}\alpha ))-2*{\sqrt {(}}2)*{\sqrt {(}}\alpha )*_{C}2^{2}*tan(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/45ec4c325c65e040daeaa2aa22fc3371d470b8d3)
![{\displaystyle u(x,t)=(1/3)*(-_{C}4+\alpha *_{C}3^{3}+\alpha *_{C}3^{3}*_{C}1^{2})/(\alpha *_{C}3)-2*_{C}3^{2}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2},v(x,t)=-(1/3)*{\sqrt {(}}12*\alpha *_{C}3^{4}*_{C}1^{2}+12*\alpha *_{C}3^{4}+6*_{C}3*_{C}4)*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,_{C}1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7fdc27dd2c266052d0346b6918e576aacff4ac56)
![{\displaystyle u(x,t)=(1/3)*(-_{C}4+\alpha *_{C}3^{3}+\alpha *_{C}3^{3}*_{C}1^{2})/(\alpha *_{C}3)-2*_{C}3^{2}*_{C}1^{2}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2},v(x,t)=-(1/3)*{\sqrt {(}}12*\alpha *_{C}3^{4}*_{C}1^{2}+12*\alpha *_{C}3^{4}+6*_{C}3*_{C}4)*_{C}1*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a3175b6276e073f74fab7e5c146b74c0b606c0e7)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
行波图
Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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Coupled KdV equation traveling wave plot
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参考文献
- ^ 李志斌编著 《非线性数学物理方程的行波解》 38页 科学出版社 2008
- *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. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press
- Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
- Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
- Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
- Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
- Dongming Wang, Elimination Practice,Imperial College Press 2004
- David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
- George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759