查看“︁DSW 方程”︁的源代码

'''DSW 方程'''(Drinfeld-Solokov-Wilson  equation)是一组非线性偏微分方程<ref>Esmaeil Alibeiki and Ahmad Neyrameh Application of Homotopy Perturbation Method to Nonlinear Drinfeld-Sokolov-Wilson Equation</ref>：

<math>\frac{\partial u}{\partial t}+3*v*\frac{\partial v}{\partial x}=0</math>

<math>\frac{\partial v}{\partial t}-2*\frac{\partial^3 v}{\partial x^3}+\frac{\partial u}{\partial x}*v+2u*\frac{\partial v}{\partial x}</math>

==解析解==
DSW方程有多种解析解<ref>Esmaeil Alibeiki and Ahmad Neyrameh Application of Homotopy Perturbation Method to
Nonlinear Drinfeld-Sokolov-Wilson Equation</ref>
===对称消减法===
[[File:DSW Equation symmetry reduction method animation.gif|thumb|left|200px|DSW Equation symmetry reduction method animation]]
用减对称法可求DSW方程的解析解<ref>B.Kauer, Symmetry Reduction Mothod for Exact Solution of some Nonlinear Systems p27</ref>

<math>u(x,t) := -sqrt(2*m)*c2*tanh(c1+c2*(m*t-x))</math>

参数：c2 = .5, c1 = 1.4, m = 2.3

<math>u(x,t)=-.758*sqrt(2)*tanh(1.4+1.15*t-.5*x)</math>

===变分法===
[[File:DSW Equation variational method animation.gif|thumb|200px|DSW Equation variational method animation]]
<math>u(x,t)=f := (3*c*(1/2))*sech(\sqrt{(1/2)*c}*(x-c*t))^2</math><ref>Wei-Min Zhang Solitary Solutions and Singular Periodic Solutions of the Drinfeld-Sokolov-Wilson Equation by Variational Approach,Applied Mathematical Sciences, Vol. 5, 2011, no. 38, 1887 - 1894</ref>。

===达布变换法===
利用[[达布变换]]可求DSW方程的解析解<ref>耿献国、吴丽华《Darboux Transformation and Explicit Solutions for Drinfeld–Sokolov–Wilson Equation</ref>

<math>v := -(1/2)*k^2*(-1+\sqrt(3)*tanh(k^3*t+(1/2)*k*y)*cot((1/2)*\sqrt(3)*k*y))</math>
[[File:DSW breather with Dabourx transform.gif|thumb|200px|left|DSW breather with Dabourx transform]]

==同伦法==
[[File:Drinfeld-Sokolov-Wilson Equation Homotopy method animation.gif|thumb|200px|Drinfeld-Sokolov-Wilson Equation Homotopy method animation]]
利用[[同伦#函数的同伦|函数的同伦]]，可求DSW方程的解析解<ref>Esmaeil Alibeiki and Ahmad Neyrameh,Application of Homotopy Perturbation Method to Nonlinear Drinfeld-Sokolov-Wilson Equation</ref>。

<math>u(x,t)=-360*t^2*sec(x)^2*tan(x)^4-396*t^2*sec(x)^2*tan(x)</math>
<math>-60*t^2*sec(x)^2+360*t^2*sec(x)^4*tan(x)^2+72*t^2*sec(x)^4</math>

==行波分析法==
{{Gallery
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|File:DSW equation traveling wave plot6.gif|
|File:DSW equation traveling wave plot7.gif|
|File:DSW equation traveling wave plot8.gif|
|File:DSW equation traveling wave plot10.gif|
|File:DSW equation traveling wave plot12.gif|
|File:DSW equation traveling wave plot14.gif|
}}

==参考文献==
<references/>
# *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


{{非线性偏微分方程}}
[[category:非线性偏微分方程]]
[[category:孤立子]]