查看“︁扎哈罗夫-库兹涅佐夫方程”︁的源代码


'''扎哈罗夫-库兹涅佐夫方程'''（Zhakharov-Kutznezov equation)是一个非线性偏微分方程<ref>Touqeer Nawaza, 
Ahmet Yıldırımb, Syed Tauseef Mohyud-Din：Analytical solutions Zakharov–Kuznetsov equations,Advanced Powder Technology,Volume 24, Issue 1, January 2013, Pages 252–256</ref>。




<math>\frac{\partial u}{\partial t}+a*u(x,y,t)*\frac{\partial u}{\partial x}+b*u^2(x,y,t)*\frac{\partial u}{\partial x}+c*\frac{\partial^3 u}{\partial x^3}+d*\frac{\partial^3 u}{\partial x\partial y^2}=0</math>

==解析解==
扎哈罗夫-库兹涅佐夫方程有许多解析解，包括<ref>YAN Zhi-Lian and LIU Xi-Qiang Symmetry Reductions and Explicit Solutions for a Generalized Zakharov Kuznetsov Equation,Commun. Theor. Phys. (Beijing, China) 45 (2006) pp. 29–32</ref>

<math>u[1] := i/((l*\xi+m*\eta)*t^(1/3))-1/(2*b)</math>

:<math>u[4] := \sqrt(-a2/a[4])*sec(\sqrt(-a2)*(l*\xi+m*\eta))</math>

:<math>u[5] := e*\sqrt(a2/a4)*tan(\sqrt((1/2)*a2)*(l*\xi+m*\eta))</math>
:<math>u[7] := -a1/(2*a2)+e*a1*sinh(2*\sqrt(a2)*(l*\xi+m*\eta))/(2*a2)</math>
:<math>u[8] := e*\sqrt(-a2/a4)*tanh(\sqrt(-(1/2)*a2)*(l*\xi+m*\eta))</math>
:<math>u[9] := -a2*sech(\sqrt((1/2)*a2)*(l*\xi+m*\eta))^2/a3</math>
:<math>u[11] := 1/(a3*(l*\xi+m*\eta)^2)</math>

其中

<math>\xi := x/t^(1/3)+a^2*t^(2/3)/(4*b)+3*c[4]/(c[1]*t^(1/3))</math>

<math>\eta := y/t^(1/3)+3*c[3]/(c[1]*t^(1/3))</math>

<math>b := -6*(c*l^2+d*m^2)</math>

参数：params := a1 = 1, a2 = 1, a3 = 2.3, a4 = 3.4, d = 1.2, e = 1.3, m = 5.35, c[1] = 5.22, c[2] = 3.23, c[3] = 1.3, c3 = 3.33, c[4] = 1.35, c4 = 1.44, l = 2.1, a[1] = 3.1, a[2] = 3.23, a0 = 5.34, a = .7, c = 1.1；

{{Gallery
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|File:Zakharov-Kutznezov equation plot1.gif|Zakharov-Kutznezov equation plot1
|File:Zakharov-Kutznezov equation plot4.gif|Zakharov-Kutznezov equation plot4
|File:Zakharov-Kutznezov equation plot5.gif|Zakharov-Kutznezov equation plot5
|File:Zakharov-Kutznezov equation plot7.gif|Zakharov-Kutznezov equation plot7
|File:Zakharov-Kutznezov equation plot8.gif|Zakharov-Kutznezov equation plot8
|File:Zakharov-Kutznezov equation plot9.gif|Zakharov-Kutznezov equation plot9
|File:Zakharov-Kutznezov equation plot11.gif|Zakharov-Kutznezov equation plot11
}}

==参考文献==
{{非线性偏微分方程}}
<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

[[category:非线性偏微分方程]]
[[category:孤立子]]