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

R. Sabry; M. A. Zahran; Engui Fan

doi:10.1016/j.physleta.2004.04.002

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

R. Sabry
, M. A. Zahran
, Engui Fan

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	93-101
Number of pages	9
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	326
Issue number	1-2
DOIs	https://doi.org/10.1016/j.physleta.2004.04.002
State	Published - 31 May 2004
Externally published	Yes

Keywords

Cylindrical KdV equation
Generalized expansion method
Generalized KdV equation with variable coefficients
Jacobi and Weierstrass doubly periodic wave solutions
Solitary wave solutions
Symbolic computation

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10.1016/j.physleta.2004.04.002

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

abstract = "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.",

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AU - Sabry, R.

AU - Zahran, M. A.

AU - Fan, Engui

PY - 2004/5/31

Y1 - 2004/5/31

N2 - 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.

AB - 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.

KW - Cylindrical KdV equation

KW - Generalized expansion method

KW - Generalized KdV equation with variable coefficients

KW - Jacobi and Weierstrass doubly periodic wave solutions

KW - Solitary wave solutions

KW - Symbolic computation

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SN - 0375-9601

VL - 326

SP - 93

EP - 101

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1-2

ER -

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

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Keywords

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