别洛乌索夫-扎伯廷斯基方程(Belousov-Zhabotinsky equation)是一组模拟化学反应扩散的非线性偏微分方程[1]:
解析解[编辑]
![{\displaystyle u(x,t)=1/(4*(1+r))-(1/2)*coth(_{C}1-(1/12)*{\sqrt {(}}6)*x/{\sqrt {(}}d)-(5/12)*t)/(1+r)+(1/4)*coth(_{C}1-(1/12)*{\sqrt {(}}6)*x/sqrt(d)-(5/12)*t)^{2}/(1+r)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f159b21e883df7d23e38ced157b23f662629e19b)
![{\displaystyle u(x,t)=1/(4*(1+r))-(1/2)*tanh(_{C}1-(1/12)*{\sqrt {(}}6)*x/{\sqrt {(}}d)-(5/12)*t)/(1+r)+(1/4)*tanh(_{C}1-(1/12)*{\sqrt {(}}6)*x/sqrt(d)-(5/12)*t)^{2}/(1+r)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/abe2ede0e2ce2e6f2f54be47cb7361bafe28a4aa)
![{\displaystyle u(x,t)=1/(4*(1+r))-(1/2*I)*cot(_{C}1-(1/2)*x/{\sqrt {(}}-6*d)-(5/12*I)*t)/(1+r)-(1/4)*cot(_{C}1-(1/2)*x/{\sqrt {(}}-6*d)-(5/12*I)*t)^{2}/(1+r)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2905cb68bc9d0b7926d5d268a48d33c68e9a8d1a)
![{\displaystyle u(x,t)=1/(4*(1+r))-(1/2*I)*tan(_{C}1-(1/2)*x/{\sqrt {(}}-6*d)+(5/12*I)*t)/(1+r)-(1/4)*tan(_{C}1-(1/2)*x/{\sqrt {(}}-6*d)+(5/12*I)*t)^{2}/(1+r)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7b06335529b74f6140447588f110ebba8a6699b4)
![{\displaystyle u(x,t)=1/(4*(1+r))-(1/2*I)*tan(_{C}1+(1/2)*x/{\sqrt {(}}-6*d)+(5/12*I)*t)/(1+r)-(1/4)*tan(_{C}1+(1/2)*x/{\sqrt {(}}-6*d)+(5/12*I)*t)^{2}/(1+r)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d16336a84c7f7e17e3998efc493a37a86da39093)
行波图[编辑]
Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky equation traveling wave plot
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Belousov-Zhabotinsky 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》 110-112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