查看“︁K(n,n)方程”︁的源代码

''' K(n,n)方程'''是一个非线性偏微分方程：<ref>Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS,（《非线性偏微分方程手册》） SECOND EDITION p891 CRC PRESS</ref>

<math> u_{t}+a*(u^n)_{x}+(u^n)_{xxx}=0   </math>

==解析解==
*当 a>0
:: <math> u(x,t)= \left( \frac{2cn}{a(n+1)} \sin^2 \left(\frac{n-1}{2n}\sqrt{a}(x-ct+b)\right)\right)^{1/(n-1)} </math>
*当 ''a''&nbsp;<&nbsp;0
:: <math> u(x,t)=\left( \frac{2cn}{a(n+1)}\sinh^2\left(\frac{n-1}{2n}\sqrt{-a}(x-ct+b)\right)\right)^{1/(n-1)} </math>

:: <math> u(x,t)= \left( \frac{2cn}{a(n+1)} \cosh^2 \left(\frac{n-1}{2n}\sqrt{-a}(x-ct+b)\right)\right)^{1/(n-1)} </math>

==行波图==
{|
|[[File:K(n,n) equation traveling wave plot 1.gif|frame|K(n,n) 方程行波图]]
|[[File:K(n,n) equation traveling wave plot 2.gif|frame|K(n,n) 方程行波图]]
|}

==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

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