正则长波方程(Regularized long wave equation)是一个非线性偏微分方程:[1]
当 α=1,μ=1,正则长波方程即本杰明-博纳-马奥尼方程。
解析解
![{\displaystyle {u(x,t)=-(_{C}5+_{C}4)/(\alpha *_{C}4)+12*\mu *_{C}5*_{C}4*WeierstrassP(_{C}3+_{C}4*x+_{C}5*t,_{C}2,_{C}1)/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf134750d28617e0c368f50beea462a2416baee)
![{\displaystyle {u(x,t)=(4*\mu *_{C}3*_{C}2^{2}-_{C}3-_{C}2)/(\alpha *_{C}2)+12*\mu *_{C}3*_{C}2*csch(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/95adb7b5979e1c81cc5611724ea9cf816e241e49)
![{\displaystyle {u(x,t)=(4*\mu *_{C}3*_{C}2^{2}-_{C}3-_{C}2)/(\alpha *_{C}2)-12*\mu *_{C}3*_{C}2*sech(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ffda93cc202788799c3e64d80aa09de216c1dba)
![{\displaystyle {u(x,t)=-(4*\mu *_{C}3*_{C}2^{2}+_{C}3+_{C}2)/(\alpha *_{C}2)+12*\mu *_{C}3*_{C}2*csc(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8ece48b4b8645cbc38201f10a41f7e58e15d6604)
![{\displaystyle {u(x,t)=(-4*\mu *_{C}4*_{C}3^{2}-_{C}4-_{C}3+8*\mu *_{C}4*_{C}3^{2}*_{C}1^{2})/(\alpha *_{C}3)-12*\mu *_{C}4*_{C}3*_{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/f6b28cf74eca721f9c4b09c48dfd03d36ac09cb6)
![{\displaystyle {u(x,t)=(-4*\mu *_{C}4*_{C}3^{2}-_{C}4-_{C}3+8*\mu *_{C}4*_{C}3^{2}*_{C}1^{2})/(\alpha *_{C}3)-12*\mu *_{C}4*_{C}3*(-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/bfd3000a19cc5a43f4f143cfa9138c3e5885c7f9)
![{\displaystyle {u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+_{C}4+_{C}3-8*\mu *_{C}4*_{C}3^{2})/(\alpha *_{C}3)-12*\mu *_{C}4*_{C}3*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2837f54e9b2bb94f3d2533c51a7eec4e3decdd42)
![{\displaystyle {u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+_{C}4+_{C}3-8*\mu *_{C}4*_{C}3^{2})/(\alpha *_{C}3)+12*\mu *_{C}4*_{C}3*(-1+_{C}1^{2})*JacobiND(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9acecf56d66a92381643c78984c7c7c8fad20f9b)
![{\displaystyle {u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+4*\mu *_{C}4*_{C}3^{2}+_{C}4+_{C}3)/(\alpha *_{C}3)+12*\mu *_{C}4*_{C}3*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6fd45aac96ace52c7ef626feb2d005904edf9a05)
![{\displaystyle {u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+4*\mu *_{C}4*_{C}3^{2}+_{C}4+_{C}3)/(\alpha *_{C}3)+12*\mu *_{C}4*_{C}3*_{C}1^{2}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9ac59a18a115dea08312c1e11931a7f4b8289e9)
行波图
正则长波方程行波图
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正则长波方程行波图
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正则长波方程行波图
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正则长波方程行波图
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正则长波方程行波图
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正则长波方程行波图
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正则长波方程行波图
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正则长波方程行波图
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正则长波方程行波图
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正则长波方程行波图
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正则长波方程行波图
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参考文献
- ^ Griffith, chapter 13, p239-260
- 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