A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation

被引：45

作者：

Sabry, R ^{[1
]}

Zahran, MA

Fan, EG

机构：

[1] Mansoura Univ, Fac Sci, Dept Phys, Theoret Phys Grp, Dumyat 34517, Egypt

[2] Mansoura Univ, Fac Sci, Dept Phys, Theoret Phys Grp, Mansoura 35516, Egypt

[3] Fudan Univ, Inst Math, Key Lab Nonlinear Math Models & Methods, Shanghai 200433, Peoples R China

来源：

PHYSICS LETTERS A | 2004年 / 326卷 / 1-2期

关键词：

generalized expansion method; generalized KdV equation with variable coefficients; cylindrical KdV equation; solitary wave solutions; Jacobi and Weierstrass doubly periodic wave solutions; symbolic computation;

D O I：

10.1016/j.physleta.2004.04.002

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：93 / 101

页数：9

共 20 条

[1] Akhiezer N. I., 1990, Elements of the Theory of Elliptic Functions
[2] SOLUTION BY SPECTRAL-TRANSFORM METHOD OF A NON-LINEAR EVOLUTION EQUATION INCLUDING AS A SPECIAL CASE CYLINDRICAL KDV EQUATION
CALOGERO, F
DEGASPERIS, A
[J]. LETTERE AL NUOVO CIMENTO, 1978, 23 (04): : 150 - 154
[3] New exact solutions for a generalized variable coefficients 2D KdV equation
Elwakil, SA
El-Labany, SK
Zahran, MA
Sabry, R
[J]. CHAOS SOLITONS & FRACTALS, 2004, 19 (05) : 1083 - 1086
[4] An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations
Fan, EG
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (25): : 7009 - 7026
[5] Extended tanh-function method and its applications to nonlinear equations
Fan, EG
[J]. PHYSICS LETTERS A, 2000, 277 (4-5) : 212 - 218
[6] Auto-Backlund transformation and similarity reductions for general variable coefficient KdV equations
Fan, EG
[J]. PHYSICS LETTERS A, 2002, 294 (01) : 26 - 30
[7] Traveling wave solutions for nonlinear equations using symbolic computation
Fan, EG
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2002, 43 (6-7) : 671 - 680
[8] SLOWLY VARYING SOLITARY WAVES .1. KORTEWEG-DE-VRIES EQUATION
GRIMSHAW, R
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1979, 368 (1734) : 359 - 375
[9] EXACT SOLITARY WAVE SOLUTIONS OF COUPLED NONLINEAR EVOLUTION-EQUATIONS USING MACSYMA
HEREMAN, W
[J]. COMPUTER PHYSICS COMMUNICATIONS, 1991, 65 (1-3) : 143 - 150
[10] EXACT SOLUTION OF KORTEWEG-DE VRIES EQUATION FOR MULTIPLE COLLISIONS OF SOLITONS
HIROTA, R
[J]. PHYSICAL REVIEW LETTERS, 1971, 27 (18) : 1192 - +

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