mKdV方程是一個非線性偏微分方程:[1]
解析解[編輯]
![{\displaystyle u(x,t)={\sqrt {(}}6)*_{C}2*sech(_{C}1+_{C}2*x-_{C}2^{3}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/06bf82b3173cdad825b5090265b2e8f85a8d7acd)
![{\displaystyle u(x,t)={\sqrt {(}}6)*_{C}3*JacobiDN(_{C}2+_{C}3*x+(-2*_{C}3^{3}+_{C}3^{3}*_{C}1^{2})*t,_{C}1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/778d44013defd246998732e66cf08feafb8d0359)
![{\displaystyle u(x,t)={\sqrt {(}}-6+6*_{C}1^{2})*_{C}3*JacobiNC(-_{C}2-_{C}3*x-(_{C}3^{3}-2*_{C}3^{3}*_{C}1^{2})*t,_{C}1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3fecfe0f418e81eb94f26fe868abc914b722d747)
![{\displaystyle u(x,t)={\sqrt {(}}6-6*_{C}1^{2})*_{C}3*JacobiND(_{C}2+_{C}3*x+(-2*_{C}3^{3}+_{C}3^{3}*_{C}1^{2})*t,_{C}1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d4a4b5f1ced2c2be05b34395bb2cfbdd34cc833)
![{\displaystyle u(x,t)={\sqrt {(}}6)*_{C}1*_{C}3*JacobiCN(-_{C}2-_{C}3*x-(_{C}3^{3}-2*_{C}3^{3}*_{C}1^{2})*t,_{C}1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aa4768191de08b8452d352fc79e6a6bdd37b8cfe)
![{\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*cot(_{C}1+_{C}2*x-2*_{C}2^{3}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87c89b589274d587d93656e7ec542f5f9e1c3f2b)
![{\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*coth(_{C}1+_{C}2*x+2*_{C}2^{3}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ebfc79aa4491a2f29c7c0f03fc5418682dfe6016)
![{\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*csc(_{C}1+_{C}2*x+_{C}2^{3}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/06c135a2f9ffa5c271c0ee5bf076f3284bc60df5)
![{\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*tanh(_{C}1+_{C}2*x+2*_{C}2^{3}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5407207745abff537ad73fcd7da7269f87176941)
![{\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*sec(_{C}1+_{C}2*x+_{C}2^{3}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/357d414d099f6167377b7636293ac235f171db13)
![{\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*csch(_{C}1+_{C}2*x-_{C}2^{3}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/02ce2ba8712154c7296f2bd82c7ea9f8b3f9d96f)
![{\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)
行波圖[編輯]
mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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mKdV equation traveling wave plot
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參考文獻[編輯]
- ^ 李志斌編著 《非線性數學物理方程的行波解》 頁 科學出版社 2008
- *谷超豪 《孤立子理論中的達布變換及其幾何應用》 上海科學技術出版社
- *閻振亞著 《複雜非線性波的構造性理論及其應用》 科學出版社 2007年
- 李志斌編著 《非線性數學物理方程的行波解》 科學出版社
- 王東明著 《消去法及其應用》 科學出版社 2002
- *何青 王麗芬編著 《Maple 教程》 科學出版社 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