查看“︁纽厄尔-怀特海德方程”︁的源代码

'''纽厄尔-怀特海德方程'''（Newell-Whitehead equation)是一个非线性偏微分方程<ref>{{Cite web |url=http://eqworld.ipmnet.ru/en/solutions/npde/npde-toc1.htm |title=Newell--Whitehead equation |access-date=2014-01-25 |archive-date=2019-07-18 |archive-url=https://web.archive.org/web/20190718113336/http://eqworld.ipmnet.ru/en/solutions/npde/npde-toc1.htm |dead-url=no }}</ref>：

<math>u_{t}-u_{xx}-\alpha*u+beta*u^3=0</math>
==行波解==
纽厄尔-怀特海德方程有行波解：
:<math>u(x, t) = 1/\sqrt(\beta)</math>, 
:<math>u(x, t) = -1/\sqrt(\beta)</math>, 
:<math>u(x, t) = -(1/2*I)/\sqrt(-\beta)-(1/2)*cot(_C1-(1/4*I)*\sqrt(2)*x-(3/4*I)*t)/\sqrt(-\beta)</math>,
: <math>u(x, t) = -(1/2*I)/\sqrt(-\beta)+(1/2)*cot(_C1-(1/4*I)*\sqrt(2)*x+(3/4*I)*t)/\sqrt(-\beta)</math>, 
:<math>u(x, t) = -(1/2*I)/\sqrt(-\beta)-(1/2)*cot(_C1+(1/4*I)*\sqrt(2)*x-(3/4*I)*t)/\sqrt(-\beta)</math>, 
:<math>u(x, t) = -(1/2*I)/\sqrt(-\beta)+(1/2)*cot(_C1+(1/4*I)*\sqrt(2)*x+(3/4*I)*t)/\sqrt(-\beta)</math>, 
:<math>u(x, t) = -(1/2*I)/\sqrt(-\beta)+(1/2)*tan(_C1-(1/4*I)*\sqrt(2)*x-(3/4*I)*t)/\sqrt(-\beta)</math>,
: <math>u(x, t) = -(1/2*I)/\sqrt(-\beta)-(1/2)*tan(_C1-(1/4*I)*\sqrt(2)*x+(3/4*I)*t)/\sqrt(-\beta)</math>,
: <math>u(x, t) = -(1/2*I)/\sqrt(-\beta)+(1/2)*tan(_C1+(1/4*I)*\sqrt(2)*x-(3/4*I)*t)/\sqrt(-\beta)</math>, 
:<math>u(x, t) = -(1/2*I)/\sqrt(-\beta)-(1/2)*tan(_C1+(1/4*I)*\sqrt(2)*x+(3/4*I)*t)/\sqrt(-\beta)</math>, 
:<math>u(x, t) = (1/2*I)/\sqrt(-\beta)+(1/2)*cot(_C1-(1/4*I)*\sqrt(2)*x-(3/4*I)*t)/\sqrt(-\beta)</math>,
: <math>u(x, t) = (1/2*I)/\sqrt(-\beta)-(1/2)*cot(_C1-(1/4*I)*\sqrt(2)*x+(3/4*I)*t)/\sqrt(-\beta)</math>, 
:<math>u(x, t) = (1/2*I)/\sqrt(-\beta)+(1/2)*cot(_C1+(1/4*I)*\sqrt(2)*x-(3/4*I)*t)/\sqrt(-\beta)</math>,
: <math>u(x, t) = (1/2*I)/\sqrt(-\beta)-(1/2)*cot(_C1+(1/4*I)*\sqrt(2)*x+(3/4*I)*t)/\sqrt(-\beta)</math>, 
:<math>u(x, t) = (1/2*I)/\sqrt(-\beta)-(1/2)*tan(_C1-(1/4*I)*\sqrt(2)*x-(3/4*I)*t)/\sqrt(-\beta)</math>, 
:<math>u(x, t) = (1/2*I)/\sqrt(-\beta)+(1/2)*tan(_C1-(1/4*I)*\sqrt(2)*x+(3/4*I)*t)/\sqrt(-\beta)</math>,
: <math>u(x, t) = (1/2*I)/\sqrt(-\beta)-(1/2)*tan(_C1+(1/4*I)*\sqrt(2)*x-(3/4*I)*t)/\sqrt(-\beta)</math>,
: <math>u(x, t) = (1/2*I)/\sqrt(-\beta)+(1/2)*tan(_C1+(1/4*I)*\sqrt(2)*x+(3/4*I)*t)/\sqrt(-\beta)</math>,
: <math>u(x, t) = -1/(2*\sqrt(\beta))+(1/2)*coth(_C1-(1/4)*\sqrt(2)*x-(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = -1/(2*\sqrt(\beta))-(1/2)*coth(_C1-(1/4)*\sqrt(2)*x+(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = -1/(2*\sqrt(\beta))+(1/2)*coth(_C1+(1/4)*\sqrt(2)*x-(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = -1/(2*\sqrt(\beta))-(1/2)*coth(_C1+(1/4)*\sqrt(2)*x+(3/4)*t)/\sqrt(\beta)</math>,
: <math>u(x, t) = -1/(2*\sqrt(\beta))+(1/2)*tanh(_C1-(1/4)*\sqrt(2)*x-(3/4)*t)/\sqrt(\beta)</math>,
: <math>u(x, t) = -1/(2*\sqrt(\beta))-(1/2)*tanh(_C1-(1/4)*\sqrt(2)*x+(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = -1/(2*\sqrt(\beta))+(1/2)*tanh(_C1+(1/4)*\sqrt(2)*x-(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = -1/(2*\sqrt(\beta))-(1/2)*tanh(_C1+(1/4)*\sqrt(2)*x+(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = 1/(2*\sqrt(\beta))-(1/2)*coth(_C1-(1/4)*\sqrt(2)*x-(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = 1/(2*\sqrt(\beta))+(1/2)*coth(_C1-(1/4)*\sqrt(2)*x+(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = 1/(2*\sqrt(\beta))-(1/2)*coth(_C1+(1/4)*\sqrt(2)*x-(3/4)*t)/\sqrt(\beta)</math>,
: <math>u(x, t) = 1/(2*\sqrt(\beta))+(1/2)*coth(_C1+(1/4)*\sqrt(2)*x+(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = 1/(2*\sqrt(\beta))-(1/2)*tanh(_C1-(1/4)*\sqrt(2)*x-(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = 1/(2*\sqrt(\beta))+(1/2)*tanh(_C1-(1/4)*\sqrt(2)*x+(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = 1/(2*\sqrt(\beta))-(1/2)*tanh(_C1+(1/4)*\sqrt(2)*x-(3/4)*t)/\sqrt(\beta)</math>, 
:<math>u(x, t) = 1/(2*\sqrt(\beta))+(1/2)*tanh(_C1+(1/4)*\sqrt(2)*x+(3/4)*t)/\sqrt(\beta)</math></math>

==行波图==
{{Gallery
|width=250
|height=200
|align=center
|File:Newell-Whitehead equation traveling wave plot4.gif|
|File:Newell-Whitehead equation traveling wave plot7.gif|
|File:Newell-Whitehead equation traveling wave plot9.gif|
|File:Newell-Whitehead equation traveling wave plot3.gif|
|File:Newell-Whitehead equation traveling wave plot21.gif|
|File:Newell-Whitehead equation traveling wave plot23.gif|
|File:Newell-Whitehead equation traveling wave plot24.gif|
|File:Newell-Whitehead equation traveling wave plot25.gif|
|File:Newell-Whitehead equation traveling wave plot26.gif|
|File:Newell-Whitehead equation traveling wave plot31.gif|
}}

==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]]