博欣内斯克型方程(Boussinesq type 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}5^{2}+_{C}4^{2})/(\alpha *_{C}4^{2})+6*\beta *_{C}5^{2}*WeierstrassP(_{C}3+_{C}4*x+_{C}5*t,_{C}2,_{C}1)/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5970a389cf1e361c18db79fd3f642b6a983ab5f0)
![{\displaystyle {u(x,t)=-(1/2)*(-_{C}3^{2}+8*\beta *_{C}3^{2}*_{C}2^{2}+_{C}2^{2})/(\alpha *_{C}2^{2})+6*\beta *_{C}3^{2}*coth(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c59f33b025853ae15d18cd1384161b0394c23d2a)
![{\displaystyle u(x,t)=-(1/2)*(-_{C}3^{2}+8*\beta *_{C}3^{2}*_{C}2^{2}+_{C}2^{2})/(\alpha *_{C}2^{2})+6*\beta *_{C}3^{2}*tanh(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/73ba089f7cf165979ab110b4d619b653b68178a6)
![{\displaystyle u(x,t)=(1/2)*(_{C}3^{2}-_{C}2^{2}+4*\beta *_{C}3^{2}*_{C}2^{2})/(\alpha *_{C}2^{2})+6*\beta *_{C}3^{2}*csch(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe615feb877574df1506caae9a095c96db0fbf26)
![{\displaystyle {u(x,t)=(1/2)*(_{C}3^{2}-_{C}2^{2}+4*\beta *_{C}3^{2}*_{C}2^{2})/(\alpha *_{C}2^{2})-6*\beta *_{C}3^{2}*sech(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0fabd4c27cd335ad1ec5bcc5232bcd2a288322a1)
![{\displaystyle {u(x,t)=(1/2)*(_{C}3^{2}+8*\beta *_{C}3^{2}*_{C}2^{2}-_{C}2^{2})/(\alpha *_{C}2^{2})+6*\beta *_{C}3^{2}*cot(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91491a557758a976c29d31ee70babdf54cdb9b98)
![{\displaystyle u(x,t)=(1/2)*(-_{C}3^{2}+8*\beta *_{C}4^{2}*_{C}3^{2}*_{C}1^{2}-4*\beta *_{C}4^{2}*_{C}3^{2}+_{C}4^{2})/(\alpha *_{C}3^{2})-6*\beta *_{C}4^{2}*_{C}1^{2}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0b56c1b8a32dac782a21fea1ec05436f8cf09ad)
![{\displaystyle u(x,t)=(1/2)*(-_{C}3^{2}+8*\beta *_{C}4^{2}*_{C}3^{2}*_{C}1^{2}-4*\beta *_{C}4^{2}*_{C}3^{2}+_{C}4^{2})/(\alpha *_{C}3^{2})-6*\beta *_{C}4^{2}*(-1+_{C}1^{2})*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/8caa44f2e6231bcc395b4924e9a124c0e6393120)
![{\displaystyle {u(x,t)=-(1/2)*(_{C}3^{2}-8*\beta *_{C}4^{2}*_{C}3^{2}-_{C}4^{2}+4*\beta *_{C}4^{2}*_{C}3^{2}*_{C}1^{2})/(\alpha *_{C}3^{2})-6*\beta *_{C}4^{2}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0402114bfbb7b94c7b0ec219dd7beb0cdb684382)
行波图[编辑]
博欣内斯克型方程行波图
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博欣内斯克型方程行波图
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博欣内斯克型方程行波图
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博欣内斯克型方程行波图
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博欣内斯克型方程行波图
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博欣内斯克型方程行波图
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博欣内斯克型方程行波图
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博欣内斯克型方程行波图
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博欣内斯克型方程行波图
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参考文献[编辑]
- ^ Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS,(《非线性偏微分方程手册》) SECOND EDITION p1028 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