色散長波方程組 ((2+1)D dispersive long wave equation)是一個二元非線性偏微分方程組:[1].
解析解[編輯]
![{\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-2.*_{C}3*sec(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t),v(x,t)=_{C}4*_{C}3-2.*_{C}4*_{C}3*sec(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t)^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d965aefbebfce3742d18b0302f6b70d27cd8a1cc)
![{\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3+2.*_{C}3*sec(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t),v(x,t)=_{C}4*_{C}3-2.*_{C}4*_{C}3*sec(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t)^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e6929864400f37be7dbf293ac361d9313fe07be8)
![{\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-1.414*_{C}3*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,.707),v(x,t)=-1.*_{C}4*_{C}3*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,.707)^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7f0bb8b8ec4535526b6e4649570c92c1ce50b967)
![{\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-1.414*_{C}3*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,.707),v(x,t)=-1.*_{C}4*_{C}3*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,.70710678118654752440)^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f8446169826fccac65c2284f714be28b74c6bb2)
![{\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-2.*_{C}3*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,1.414),v(x,t)=-2.*_{C}4*_{C}3*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,1.414)^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3b335e3ff425dbb2e0ef71652ce981cbb063076)
![{\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-2.*{\sqrt {(}}-1.+_{C}1^{2})*_{C}3*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1),v(x,t)=-2.*_{C}4*_{C}3+_{C}4*_{C}3*_{C}1^{2}+(2.*_{C}4*_{C}3-2.*_{C}4*_{C}3*_{C}1^{2})*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1)^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e77b1aa209f60222c7528fab9612faff6a1a0e19)
![{\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3-2.*{\sqrt {(}}-1.+_{C}1^{2})*_{C}3*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1),v(x,t)=-2.*_{C}4*_{C}3+_{C}4*_{C}3*_{C}1^{2}+(2.*_{C}4*_{C}3-2.*_{C}4*_{C}3*_{C}1^{2})*JacobiND(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1)^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e77b1aa209f60222c7528fab9612faff6a1a0e19)
![{\displaystyle {u(x,y,t)=-1.*_{C}5/_{C}3+2.*{\sqrt {(}}-1.*_{C}1^{2}+1.)*_{C}3*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1),v(x,t)=-2.*_{C}4*_{C}3*_{C}1^{2}+_{C}4*_{C}3+(-2.*_{C}4*_{C}3+2.*_{C}4*_{C}3*_{C}1^{2})*JacobiNC(_{C}2+_{C}3*x+_{C}4*y+_{C}5*t,_{C}1)^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d205f797332fae5ff163191f110d33c14ed04bd2)
行波圖[編輯]
(2+1)維色散長波方程行波圖
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(2+1)維色散長波方程行波圖
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(2+1)維色散長波方程行波圖
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(2+1)維色散長波方程行波圖
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(2+1)維色散長波方程行波圖
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(2+1)維色散長波方程行波圖
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(2+1)維色散長波方程行波圖
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(2+1)維色散長波方程行波圖
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(2+1)維色散長波方程行波圖
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(2+1)維色散長波方程行波圖
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(2+1)維色散長波方程行波圖
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參考文獻[編輯]
- ^ 閻振亞 第 62頁
- *谷超豪 《孤立子理論中的達布變換及其幾何應用》 上海科學技術出版社
- *閻振亞著 《複雜非線性波的構造性理論及其應用》 科學出版社 2007年
- 李志斌編著 《非線性數學物理方程的行波解》 科學出版社
- 王東明著 《消去法及其應用》 科學出版社 2002
- *何青 王麗芬編著 《Maple 教程》 科學出版社 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