Extended fan's algebraic method and its application to KdV and variant Boussinesq equations

被引：0

作者：

Yang, Xian-Lin ^{[1
]}

Tang, Jia-Shi

机构：

[1] Hunan Univ, Coll Mech & Aerosp, Changsha 410082, Peoples R China

[2] Hunan Radio & Televis Univ, Dept Comp Sci, Changsha 410004, Peoples R China

来源：

COMMUNICATIONS IN THEORETICAL PHYSICS | 2007年 / 48卷 / 01期

关键词：

algebraic method; KdV equation; variant Boussinesq equations; polynomial complete discrimination system;

D O I：

暂无

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinear partial differential equations. The key idea of this method is to introduce an auxiliary ordinary differential equation which is regarded as an extended elliptic equation and whose degree r is expanded to the case of r > 4. The efficiency of the method is demonstrated by the KdV equation and the variant Boussinesq equations. The results indicate that the method not only offers all solutions obtained by using Fu's and Fan's methods, but also some new solutions.

引用

页码：1 / 6

页数：6

共 31 条

[1] A series of new soliton-like solutions and double-like periodic solutions of a (2+I)-dimensional dispersive long wave equation [J].

Chen, Y ;

Wang, Q .

CHAOS SOLITONS & FRACTALS, 2005, 23 (03) :801-807

[2] A generalized method and general form solutions to the Whitham-Broer-Kaup equation [J].

Chen, Y ;

Wang, Q ;

Li, BA .

CHAOS SOLITONS & FRACTALS, 2004, 22 (03) :675-682

[3] New exact traveling wave solutions for the two-dimensional KdV-Burgers and Boussinesq equations [J].

Elgarayhi, A ;

Elhanbaly, A .

PHYSICS LETTERS A, 2005, 343 (1-3) :85-89

[4] An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations [J].

Fan, EG .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (25) :7009-7026

[5] Extended tanh-function method and its applications to nonlinear equations [J].

Fan, EG .

PHYSICS LETTERS A, 2000, 277 (4-5) :212-218

[6] A direct approach with computerized symbolic computation for finding a series of traveling waves to nonlinear equations [J].

Fan, EG ;

Dai, HH .

COMPUTER PHYSICS COMMUNICATIONS, 2003, 153 (01) :17-30

[7] Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics [J].

Fan, EG .

CHAOS SOLITONS & FRACTALS, 2003, 16 (05) :819-839

[8] A series of travelling wave solutions for two variant Boussinesq equations in shallow water waves [J].

Fan, EG ;

Hon, YC .

CHAOS SOLITONS & FRACTALS, 2003, 15 (03) :559-566

[9]

Fu ZT, 2003, COMMUN THEOR PHYS, V40, P285

[10]

Fu ZT, 2003, COMMUN THEOR PHYS, V39, P531

← 1 2 3 4 →