本杰明-小野方程(Benjamin-Ono equation)是一个非线性偏微分方程:[1].
解析解[编辑]
![{\displaystyle u(x,t)=(1/2)*(-_{C}3^{2}+4*\beta *_{C}2^{4})/_{C}2^{2}+6*\beta *_{C}2^{2}*csch(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/57068dd09d8980ad71868efd99b03b99364cdcf1)
![{\displaystyle u(x,t)=(1/2)*(-_{C}3^{2}+4*\beta *_{C}2^{4})/_{C}2^{2}-6*\beta *_{C}2^{2}*sech(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7bdd68ac16a36d637553a7f064cf3eb6aa7a208d)
![{\displaystyle u(x,t)=-(1/2)*(4*\beta *_{C}2^{4}+_{C}3^{2})/_{C}2^{2}+6*\beta *_{C}2^{2}*csc(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5d9c96a7a9d8415c6aa09af3d85182060108eea7)
![{\displaystyle u(x,t)=-(1/2)*(4*\beta *_{C}2^{4}+_{C}3^{2})/_{C}2^{2}+6*\beta *_{C}2^{2}*sec(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf224a9b5c41b50339412f4aa935d850a5db7871)
![{\displaystyle u(x,t)=(1/2)*(8*\beta *_{C}2^{4}-_{C}3^{2})/_{C}2^{2}+6*b\eta *_{C}2^{2}*cot(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e1d49a115a0f4dfd6a15d9f2f8fae11bd7349d66)
![{\displaystyle u(x,t)=(1/2)*(8*\beta *_{C}2^{4}-_{C}3^{2})/_{C}2^{2}+6*b\eta *_{C}2^{2}*tan(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/644d5197efecd6d9f42d9a2992874a20bc4784ce)
![{\displaystyle u(x,t)=-(1/2)*(8*\beta *_{C}2^{4}+_{C}3^{2})/_{C}2^{2}+6*\beta *_{C}2^{2}*coth(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/64ae8df9443803155de31c01a482d6852906feba)
![{\displaystyle u(x,t)=-(1/2)*(8*\beta *_{C}2^{4}+_{C}3^{2})/_{C}2^{2}+6*\beta *_{C}2^{2}*tanh(_{C}1+_{C}2*x+_{C}3*t)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e4be6bec85a0a84bb2e802f3a5ab18d8ca648c3d)
![{\displaystyle u(x,t)=-(1/2)*(-8*\beta *_{C}3^{4}+4*\beta *_{C}3^{4}*_{C}1^{2}+_{C}4^{2})/_{C}3^{2}+(-6*\beta *_{C}3^{2}+6*\beta *_{C}3^{2}*_{C}1^{2})*JacobiND(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3df4e6486158d114dd9f968dc9fb63e93b2421f2)
![{\displaystyle u(x,t)=-(1/2)*(-8*\beta *_{C}3^{4}+4*\beta *_{C}3^{4}*_{C}1^{2}+_{C}4^{2})/_{C}3^{2}-6*\beta *_{C}3^{2}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0c0bd4e35e963c456394c43730de45a0fe959868)
![{\displaystyle u(x,t)=(1/2)*(-4*\beta *_{C}3^{4}+8*\beta *_{C}3^{4}*_{C}1^{2}-_{C}4^{2})/_{C}3^{2}+(6*\beta *_{C}3^{2}-6*\beta *_{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/94e4d1957964695649a77b035a524367701ffbca)
![{\displaystyle u(x,t)=-(1/2)*(4*\beta *_{C}3^{4}*_{C}1^{2}+_{C}4^{2}+4*\beta *_{C}3^{4})/_{C}3^{2}+6*\beta *_{C}3^{2}*_{C}1^{2}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5c7a55d02a72ac9882e50cd8c62044f5d69a3dd8)
![{\displaystyle u(x,t)=(1/2)*(-4*\beta *_{C}3^{4}+8*\beta *_{C}3^{4}*_{C}1^{2}-_{C}4^{2})/_{C}3^{2}-6*\beta *_{C}3^{2}*_{C}1^{2}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a3beead5e380b7097d047780b365a41e297ef3ae)
![{\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]
Benjamin-Ono equation traveling wave plot
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Benjamin-Ono equation traveling wave plot
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Benjamin-Ono equation traveling wave plot
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Benjamin-Ono equation traveling wave plot
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Benjamin-Ono equation traveling wave plot
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Benjamin-Ono equation traveling wave plot
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Benjamin-Ono equation traveling wave plot
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Benjamin-Ono 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》 82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