奥斯特洛夫斯基方程(Ostrovsky equation)是一个模拟海洋波浪的非线性偏微分方程:[1]
解析解[编辑]
![{\displaystyle u(x,t)=-6*_{C}2^{2}*csch(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ef05f945fb39a16d607a08eaf11465134aacfa7)
![{\displaystyle u(x,t)=-6*_{C}2^{2}*sec(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0f1e528a794bf5ca60289e44c233a18645de713)
![{\displaystyle u(x,t)=6*_{C}2^{2}*sech(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/435086a11410ea886b2757316ed8ba25267ad664)
![{\displaystyle u(x,t)=_{C}5+6*_{C}3^{2}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*sqrt((3*_{C}3^{2}+_{C}5)*(_{C}5^{2}+12*_{C}3^{4}+8*_{C}5*_{C}3^{2}))/((3*_{C}3^{2}+_{C}5)*_{C}3))^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e539c9b063855461fb138fc30240c57d41d8cf96)
![{\displaystyle u(x,t)=_{C}5-6*_{C}3^{2}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,(1/2)*sqrt((-3*_{C}3^{2}+_{C}5)*_{C}5*(_{C}5-4*_{C}3^{2}))/((-3*_{C}3^{2}+_{C}5)*_{C}3))^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7dd6c85fca9d3bd45eeb2ff7c5f8e0bbaeb1c19b)
![{\displaystyle u(x,t)=_{C}6-6*_{C}4^{2}*WeierstrassP(_{C}3+_{C}4*x+_{C}5*t,(1/3)*_{C}6^{2}/_{C}4^{4},_{C}1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3415857b64da0aca2a37d108ee828bfc42eebd0d)
![{\displaystyle u(x,t)=_{C}5-(3/2)*_{C}5*(4*_{C}3^{2}+_{C}5)*JacobiND(_{C}2+_{C}3*x+_{C}4*t,(1/2)*sqrt((3*_{C}3^{2}+_{C}5)*(_{C}5^{2}+12*_{C}3^{4}+8*_{C}5*_{C}3^{2}))/((3*_{C}3^{2}+_{C}5)*_{C}3))^{2}/(3*_{C}3^{2}+_{C}5)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9175359a4e88a164774f42f09585555e4421dabc)
![{\displaystyle u(x,t)=2*_{C}2^{2}-6*_{C}2^{2}*coth(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6798a7b63c483370c53c4f3f8ca285f26b5c2bcd)
![{\displaystyle u(x,t)=(2-4*_{C}1^{2}-2*sqrt(1-_{C}1^{2}+_{C}1^{4}))*_{C}3^{2}+(-6*_{C}3^{2}+6*_{C}3^{2}*_{C}1^{2})*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/08f2aa8b95e4913d7ab14da3d5c5cba5a02fe1e9)
![{\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]
Ostrovsky equation traveling wave plot
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Ostrovsky equation traveling wave plot
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Ostrovsky equation traveling wave plot
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Ostrovsky equation traveling wave plot
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Ostrovsky equation traveling wave plot
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Ostrovsky equation traveling wave plot
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Ostrovsky equation traveling wave plot
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Ostrovsky equation traveling wave plot
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Ostrovsky equation traveling wave plot
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Ostrovsky equation traveling wave plot
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Ostrovsky equation traveling wave plot
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参考文献[编辑]
- ^ Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p968 CRC PRESS
- *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