查看“︁变形K(n,n)方程”︁的源代码

''' 变形K(n,n)方程 '''(Modified  K(n,n) equation)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 p892 CRC PRESS</ref>

<math> u_{t}+a*(u^{n+1})_{x}+(u*(u^n)_{xx})_{x}=0   </math>

==解析解==
:<math> u(x,t)=( \frac{2*c}{a}*sin((1/2)*\sqrt{a}*(x-c*t+b))^2))^{1/n}</math>

:<math> u(x,t)=( \frac{2*c}{a}*sinh((1/2)*\sqrt{-a}*(x-c*t+b))^2))^{1/n}</math>
:<math> u(x,t)=( \frac{2*c}{a}*cosh((1/2)*\sqrt{-a}*(x-c*t+b))^2))^{1/n}</math>

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