五阶色散KdV方程(Fifth order dispersion KdV equation)是一个非线性偏微分方程:[1]。
解析解
![{\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -1680*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d7e86588415d5bcb71c54c3a4ebcee74925daf5)
![{\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -6720*_{C}3^{4}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/51900042e3e773c6414ae21e9cb3c19e96d2dc14)
![{\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -1680*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/38e5cc4f4f4562788a10dd1fb9ecfeda37bf5c11)
![{\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -6720*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/126ba97647ad72ca67827cefa302b01253eb1cf8)
![{\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/cfaacaae2c6b5df025ad0cb19044c7006a875618)
![{\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,I)^{2}/\alpha -6720*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,I)^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/046f1433c12258cda36a57a723f9550cdc017793)
![{\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+3360*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/30dcdb4ff8b6b76788efd52876533f77816eaa9b)
![{\displaystyle u(x,t)=-(_{C}4+1008*_{C}3^{5})/(\alpha *_{C}3)+6720*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{2}/\alpha -6720*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,{\sqrt {(}}2))^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/8b0ca407e6addc042655bb67267ccbe3ad8748f0)
![{\displaystyle u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+1680*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/6bd6c16703f167fbbdd770fbb7b8ee17fe79432a)
![{\displaystyle u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+840*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -420*_{C}3^{4}*JacobiND(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/35aa8773a0413e69be0d87b860e69122bf01998c)
![{\displaystyle u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+1680*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -1680*_{C}3^{4}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd5615edc337f8c121023bb9dc7328c861881b1f)
![{\displaystyle u(x,t)=-(252*_{C}3^{5}+_{C}4)/(\alpha *_{C}3)+840*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{2}/\alpha -420*_{C}3^{4}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*{\sqrt {(}}2))^{4}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b09106b70d3c765e8931a9fc85f86cd9c9177909)
行波图
五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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五阶色散KdV方程行波图
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参考文献
- ^ 李志斌 第29页
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- 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
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- 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
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- 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