查菲 - 堙方特方程(Chaffee-Infante equation)是一个非线性偏微分方程:[1]
解析解[编辑]
![{\displaystyle u(x,t)=-1/2-(1/2*I)*cot(_{C}1-(1/4)*{\sqrt {(}}-2*\lambda )*x+(3/4*I)*\lambda *t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/271786b61980166ac531201de296315c4a27661b)
![{\displaystyle u(x,t)=-1/2-(1/2*I)*tan(_{C}1-(1/4)*{\sqrt {(}}-2*\lambda )*x-(3/4*I)*\lambda *t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/027d756382556ed630ceded73f9a7e8db3e14399)
![{\displaystyle u(x,t)=-1/2+(1/2*I)*cot(_{C}1+(1/4)*{\sqrt {(}}-2*\lambda )*x-(3/4*I)*\lambda *t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cac25f42507a21fb18edd7ee0327f5a9f71b9d4a)
![{\displaystyle u(x,t)=-1/2+(1/2*I)*tan(_{C}1+(1/4)*{\sqrt {(}}-2*\lambda )*x+(3/4*I)*\lambda *t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/962130872710eae3b9bfc5a3dbd0d3ee474d748a)
![{\displaystyle u(x,t)=-1/2-(1/2)*coth(_{C}1-(1/4)*{\sqrt {(}}2)*{\sqrt {(}}\lambda )*x+(3/4)*\lambda *t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5787f9ffb113f501bd8a07a5027c8f2b6ad8f1fd)
![{\displaystyle u(x,t)=-1/2+(1/2)*tanh(_{C}1-(1/4)*{\sqrt {(}}2)*{\sqrt {(}}\lambda )*x-(3/4)*\lambda *t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ddc4a11b23a06644940fec7f4e1f084f7ed1c246)
![{\displaystyle u(x,t)=1/2-(1/2*I)*cot(_{C}1-(1/4)*{\sqrt {(}}-2*\lambda )*x-(3/4*I)*\lambda *t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe71830c7aa367350178d16a3c701a43923b836a)
![{\displaystyle u(x,t)=1/2-(1/2*I)*tan(_{C}1+(1/4)*{\sqrt {(}}-2*\lambda )*x+(3/4*I)*\lambda *t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/396f0da2ef46d9063700c411927a3c98f9a7c5a5)
![{\displaystyle u(x,t)=1/2-(1/2)*coth(_{C}1-(1/4)*{\sqrt {(}}2)*{\sqrt {(}}\lambda )*x-(3/4)*\lambda *t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7dba8ed403d5452b1e0b4672d2c9e0bba924a866)
![{\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[编辑]
Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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Chaffe-Infante equation traveling wave plot
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参考文献[编辑]
- ^ 李志斌编著 《非线性数学物理方程的行波解》 64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