查看“︁瓦克赫年科方程”︁的源代码

'''瓦克赫年科方程'''（Vakhnenko equation）是一个非线性偏微分方程：<ref>李志斌编著 《非线性数学物理方程的行波解》 页 科学出版社 2008</ref>

<math>U_{xt}+(U_{x})^2+U*U_{xx}+U=0</math>

==解析解==
:<math>p1= arctanh(coth(1.56+1.7969454312181156991*x^1.2+1.9520491881558575047*t^1.2))</math>
:<math>p2=-.14+1.4974545260150964159*x^1.2+1.6267076567965479206*t^1.2</math>
:<math>p3=3.00+1.7969454312181156991*x^1.2+1.9520491881558575047*t^1.2</math>
:<math>p4=-3.5699111843077518862+2.9949090520301928318*x^1.2+3.2534153135930958412*t^1.2</math>
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==行波图==
{|
|[[File:Vakhnennko equation traveling wave plot 1.gif|frame|Vakhnennko equation traveling wave plot]]
|[[File:Vakhnennko equation traveling wave plot 2.gif|frame|Vakhnennko equation traveling wave plot]]
|}
{|
|[[File:Vakhnennko equation traveling wave plot 3.gif|frame|Vakhnennko equation traveling wave plot]]|
|}

==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]]