瓦克赫年科方程(Vakhnenko equation)是一個非線性偏微分方程:[1]
解析解
![{\displaystyle p1=arctanh(coth(1.56+1.7969454312181156991*x^{1}.2+1.9520491881558575047*t^{1}.2))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a5c29ce30e0e637f22274bf3f9af44e6e3813916)
![{\displaystyle p2=-.14+1.4974545260150964159*x^{1}.2+1.6267076567965479206*t^{1}.2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/98aeb21a1285fd0064d94923d4cf0adae9e92ded)
![{\displaystyle p3=3.00+1.7969454312181156991*x^{1}.2+1.9520491881558575047*t^{1}.2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c28aee6b7a8eb24fe3df66556d5ef964c4266a4d)
![{\displaystyle p4=-3.5699111843077518862+2.9949090520301928318*x^{1}.2+3.2534153135930958412*t^{1}.2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b2b85421e68894375f88dea41f06be626d79620e)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
![{\displaystyle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/df4dcd61276328f7c7ec5bdc399b6e11114a2c68)
行波圖
Vakhnennko equation traveling wave plot
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Vakhnennko equation traveling wave plot
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Vakhnennko equation traveling wave plot|
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參考文獻
- ^ 李志斌編著 《非線性數學物理方程的行波解》 頁 科學出版社 2008
- *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