非规范伯格斯方程 (Unnormalized Burgers equation)是一个非线性偏微分方程:[1]
解析解
![{\displaystyle u(x,t)=_{C}3/(\beta *_{C}2)+2*\alpha *_{C}2*cot(_{C}1+_{C}2*x+_{C}3*t)/\beta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e90de20c0882318307dfefa26b69ce13b3eebf5)
![{\displaystyle {u(x,t)=_{C}3/(\beta *_{C}2)+2*\alpha *_{C}2*coth(_{C}1+_{C}2*x+_{C}3*t)/\beta }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/75e1ea97e7827ff2debd876bcd8ae6dd0d63caaf)
![{\displaystyle {u(x,t)=_{C}3/(\beta *_{C}2)-2*\alpha *_{C}2*tan(_{C}1+_{C}2*x+_{C}3*t)/\beta }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05c35e6744c426b8266a80378f5717f4702f30a6)
![{\displaystyle {u(x,t)=_{C}3/(\beta *_{C}2)+2*\alpha *_{C}2*tanh(_{C}1+_{C}2*x+_{C}3*t)/\beta }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c4a5f8d7274dfdc60d45c1211e1bcb449fbaaf3a)
![{\displaystyle {u(x,t)=(_{C}5+tanh((1/2)*_{C}1*(_{C}3+_{C}4*x+_{C}5*t-_{C}2)/(\alpha *_{C}4^{2}))*_{C}1)/(\beta *_{C}4)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe922fdcea1cc900ecf729c718492fedd6c1f651)
![{\displaystyle {u(x,t)=(_{C}5+tanh((1/2)*_{C}1*({\sqrt {(}}csc(_{C}3+_{C}4*x+_{C}5*t)-1)*{\sqrt {(}}csc(_{C}3+_{C}4*x+_{C}5*t)+1)*arctan(1/{\sqrt {(}}csc(_{C}3+_{C}4*x+_{C}5*t)^{2}-1))+_{C}2*{\sqrt {(}}csc(_{C}3+_{C}4*x+_{C}5*t)^{2}-1))/(\alpha *_{C}4^{2}*{\sqrt {(}}csc(_{C}3+_{C}4*x+_{C}5*t)^{2}-1)))*_{C}1)/(\beta *_{C}4)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a38723c9e91ae56b34e27e1e42f7cb6c90862f2a)
![{\displaystyle {u(x,t)=(_{C}5-tan((1/2)*{\sqrt {(}}2*_{C}1*\alpha *_{C}4^{3}*\beta -_{C}5^{2})*(ln(cosh(_{C}3+_{C}4*x+_{C}5*t)+{\sqrt {(}}cosh(_{C}3+_{C}4*x+_{C}5*t)^{2}-1))+_{C}2)/(\alpha *_{C}4^{2}))*{\sqrt {(}}2*_{C}1*\alpha *_{C}4^{3}*\beta -_{C}5^{2}))/(\beta *_{C}4)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/55602f976381891dc69353d930cf90eb5d6cf74f)
![{\displaystyle {u(x,t)=(_{C}5-tan((1/2)*{\sqrt {(}}2*_{C}1*\alpha *_{C}4^{3}*\beta -_{C}5^{2})*(_{C}3+_{C}4*x+_{C}5*t+_{C}2)/(\alpha *_{C}4^{2}))*{\sqrt {(}}2*_{C}1*\alpha *_{C}4^{3}*\beta -_{C}5^{2}))/(\beta *_{C}4)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8bafb8243496092d872a95c1ed6c96b4cfe3ec20)
![{\displaystyle {u(x,t)=(_{C}5+tanh((1/2)*{\sqrt {(}}2*_{C}1*\alpha *_{C}4^{3}*\beta +_{C}5^{2})*(arctanh(1/{\sqrt {(}}1+csch(_{C}3+_{C}4*x+_{C}5*t)^{2}))-_{C}2)/(\alpha *_{C}4^{2}))*{\sqrt {(}}2*_{C}1*\alpha *_{C}4^{3}*\beta +_{C}5^{2}))/(\beta *_{C}4)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a531fa44aec1ce503d9d71a8e606503df303288b)
![{\displaystyle {u(x,t)=(_{C}5-tanh((1/2)*{\sqrt {(}}2*_{C}1*\alpha *_{C}4^{3}*\beta +_{C}5^{2})*((1/2)*Pi-_{C}3-_{C}4*x-_{C}5*t+_{C}2)/(\alpha *_{C}4^{2}))*{\sqrt {(}}2*_{C}1*\alpha *_{C}4^{3}*\beta +_{C}5^{2}))/(\beta *_{C}4)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/868474db8276e1dd4cc9f2b64d0de259aec30473)
![{\displaystyle {u(x,t)=-(-_{C}5+tanh((1/2)*_{C}1*({\sqrt {(}}sec(_{C}3+_{C}4*x+_{C}5*t)-1)*{\sqrt {(}}sec(_{C}3+_{C}4*x+_{C}5*t)+1)*arctan(1/{\sqrt {(}}sec(_{C}3+_{C}4*x+_{C}5*t)^{2}-1))+_{C}2*{\sqrt {(}}sec(_{C}3+_{C}4*x+_{C}5*t)^{2}-1))/(\alpha *_{C}4^{2}*{\sqrt {(}}sec(_{C}3+_{C}4*x+_{C}5*t)^{2}-1)))*_{C}1)/(\beta *_{C}4)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ccc3d838debccbf7134a85abba17720915435806)
![{\displaystyle {u(x,t)=(1/2)*({\sqrt {(}}2)*_{C}5+2*tanh((1/2)*{\sqrt {(}}\beta *_{C}1*_{C}4*\alpha )*(_{C}3+_{C}4*x+_{C}5*t+_{C}2)*{\sqrt {(}}2)/(_{C}4*\alpha ))*_{C}4*{\sqrt {(}}\beta *_{C}1*_{C}4*\alpha ))*{\sqrt {(}}2)/(\beta *_{C}4)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/af93ae63169572f9557510f4ace295402555a14e)
行波图
非规范伯格斯方程行波图
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非规范伯格斯方程行波图
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非规范伯格斯方程行波图
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非规范伯格斯方程行波图
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非规范伯格斯方程行波图
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非规范伯格斯方程行波图
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非规范伯格斯方程行波图
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非规范伯格斯方程行波图
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非规范伯格斯方程行波图
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非规范伯格斯方程行波图
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非规范伯格斯方程行波图
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参考文献
- ^ Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS,(《非线性偏微分方程手册》) SECOND EDITION p187 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