查看“伯格斯方程”的源代码

'''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：

<math>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  </math>

==Backlund 变换==
伯格斯方程通过下列Backlund变换<ref>Inna Shingareva, Carlos Lizarraga Celaya, Solving Nonlinear Differential Equations with Maple and Mathematica, p47,Springer</ref>。

<math>w[x] = (1/2)*w*u</math>

<math> w[t] = (1/2)*w[x]*u+(1/2)*w*u[x]</math>

则化为 热方程：

<math>HEq := w[t] = w[x, x]</math>
==解析解==
伯格斯方程有钟行孤波和扭波两种形式的行波解<ref>Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple p57-58Springer</ref>

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|[[File:Burgers equation traveling wave plot 7.gif|thumb|Burgers equation traveling wave plot]]
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==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}}

[[分类:非线性偏微分方程]]