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维基百科

伯格斯方程

伯格斯方程(Burgers equation)是一个模拟冲击波的传播和反射的非线性偏微分方程:

Backlund 变换

伯格斯方程通过下列Backlund变换[1]

 

 

则化为 热方程:

 

解析解

伯格斯方程有钟行孤波和扭波两种形式的行波解[2]

 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot
 
Burgers equation traveling wave plot

参考文献

  1. ^ Inna Shingareva, Carlos Lizarraga Celaya, Solving Nonlinear Differential Equations with Maple and Mathematica, p47,Springer
  2. ^ Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple p57-58Springer
  1. *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
  2. *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
  3. 李志斌编著 《非线性数学物理方程的行波解》 科学出版社
  4. 王东明著 《消去法及其应用》 科学出版社 2002
  5. *何青 王丽芬编著 《Maple 教程》 科学出版社 2010 ISBN 9787030177445
  6. Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press
  7. Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
  8. Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
  9. Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
  10. Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
  11. Dongming Wang, Elimination Practice,Imperial College Press 2004
  12. David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
  13. George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759

伯格斯方程, burgers, equation, 是一个模拟冲击波的传播和反射的非线性偏微分方程, displaystyle, frac, partial, partial, frac, partial, partial, frac, partial, partial, backlund, 变换, 编辑通过下列backlund变换, displaystyle, displaystyle, 则化为, 热方程, displaystyle, 解析解, 编辑有钟行孤波和扭波两种形式的行波解, burgers, equat. 伯格斯方程 Burgers equation 是一个模拟冲击波的传播和反射的非线性偏微分方程 s y s u x t t u x t u x t x n u 2 u x t x 2 0 displaystyle sys frac partial u x t partial t u x t frac partial u x t partial x nu frac partial 2 u x t partial x 2 0 Backlund 变换 编辑伯格斯方程通过下列Backlund变换 1 w x 1 2 w u displaystyle w x 1 2 w u w t 1 2 w x u 1 2 w u x displaystyle w t 1 2 w x u 1 2 w u x 则化为 热方程 H E q w t w x x displaystyle HEq w t w x x 解析解 编辑伯格斯方程有钟行孤波和扭波两种形式的行波解 2 Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot Burgers equation traveling wave plot参考文献 编辑 Inna Shingareva Carlos Lizarraga Celaya Solving Nonlinear Differential Equations with Maple and Mathematica p47 Springer Inna Shingareva Carlos Lizarraga Celaya Solving Nonlinear Partial Differential Equations with Maple p57 58Springer 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 Lizarraga 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 amp Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759 取自 https zh wikipedia org w index php title 伯格斯方程 amp oldid 68602426, 维基百科,wiki,书籍,书籍,图书馆,

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