藤田-斯托姆方程(Fujita-Storm equation)是一個非線性偏微分方程:[1]
解析解
![{\displaystyle f1:=1/{\sqrt {(}}2*C1*x-2*a*C1^{2}*t+C2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/950cdb251f93d30d16d87ddd6191414409c3e2fe)
![{\displaystyle f2:=-1/{\sqrt {(}}2*C1*x-2*a*C1^{2}*t+C2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b40ea4155941048ad238c884c65509be6e3f58b7)
![{\displaystyle f3:=1/{\sqrt {(}}(1/2)*C1*(x+C2)^{2}/a+C3*\exp(C1*t))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f53928e224f9c0c57f901ee3de27e782bd235eb9)
![{\displaystyle f4:=-1/{\sqrt {(}}(1/2)*C1*(x+C2)^{2}/a+C3*\exp(C1*t))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/402511ea237ffd945e4e788d095ef72306447fdc)
![{\displaystyle f5:=1/({\sqrt {(}}c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*{\sqrt {(}}4-\exp(8*a*t)*(c*\exp(-a*t)+c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a3789cf2e57f3aad4968cab5290d264c35cb4a68)
![{\displaystyle f6:=1/({\sqrt {(}}c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*{\sqrt {(}}4-\exp(8*a*t)*(c*\exp(-a*t)-c^{2}*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t))))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/22fb00a47e9952c484a9f8677ba29be6a2a1dd7b)
![{\displaystyle f7:=-1/({\sqrt {(}}c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*{\sqrt {(}}4-\exp(8*a*t)*(c*\exp(-a*t)+c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4f7b88dbae2d0adce93bbe185e37ca5a95aed0a3)
![{\displaystyle f8:=-1/({\sqrt {(}}c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))*{\sqrt {(}}4-\exp(8*a*t)*(c*\exp(-a*t)-c^{2}*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t))))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dbace462a9970f0ca7d83cb330879be1fb4bd18e)
![{\displaystyle f9:=1/({\sqrt {(}}c^{2}*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*{\sqrt {(}}\exp(8*a*t)*(c*\exp(-a*t)+c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f72d59e721fe2361a0e72e000352bebbeda6fe3d)
![{\displaystyle f10:=1/({\sqrt {(}}c^{2}*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*{\sqrt {(}}\exp(8*a*t)*(c*\exp(-a*t)-c^{2}*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t))))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3fda5942010155aed8bf63688e27cdc70556b560)
![{\displaystyle f11:=-1/({\sqrt {(}}c^{2}*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*{\sqrt {(}}\exp(8*a*t)*(c*\exp(-a*t)+c^{2}*\exp(-2*a*t)+2*\exp(-8*a*t)+2*x*\exp(-4*a*t))))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2e28ac496872a8cbc3c729acace3294f0dccda3)
![{\displaystyle f12:=-1/({\sqrt {(}}c^{2}*\exp(2*a*t)+2*\exp(8*a*t)+2*x*\exp(4*a*t))*{\sqrt {(}}\exp(8*a*t)*(c*\exp(-a*t)-c^{2}*\exp(-2*a*t)-2*\exp(-8*a*t)-2*x*\exp(-4*a*t))))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e832b5214fc0496729ade72613d7d0cfdca313e)
行波圖
藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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藤田-斯托姆方程圖
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參考文獻
- ^ Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS,(《非線性偏微分方程手冊》) SECOND EDITION p212 CRC PRESS
- *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