Polynomials in logistic function and solitary waves of nonlinear differential equations

被引：51

作者：

Kudryashov, Nikolay A. ^{[1
]}

机构：

[1] Natl Res Nucl Univ MEPhI, Dept Appl Math, Moscow 115409, Russia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 17期

关键词：

Logistic function; Nonlinear differential equation; Exact solution; Solitary wave series; Polynomial in logistic function; TANH-FUNCTION METHOD; SIMPLEST EQUATION; MEROMORPHIC SOLUTIONS; EVOLUTION;

D O I：

10.1016/j.amc.2013.03.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Properties of polynomials in logistic function are studied. It is demonstrated that these polynomials can be used for construction of exact solutions to nonlinear differential equations. Nonlinear differential equations with exact solutions in the form of polynomials in logistic function are found. It is shown there are solitary waves of nonlinear differential equations described by polynomial in logistic function with many maximum and minimum. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：9245 / 9253

页数：9

共 39 条

[1] Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs [J].

Baldwin, D ;

Göktas, Ü ;

Hereman, W ;

Hong, L ;

Martino, RS ;

Miller, JC .

JOURNAL OF SYMBOLIC COMPUTATION, 2004, 37 (06) :669-705

[2] Solitary wave solution for the generalized Kawahara equation [J].

Biswas, Anjan .

APPLIED MATHEMATICS LETTERS, 2009, 22 (02) :208-210

[3] On elliptic solutions of nonlinear ordinary differential equations [J].

Demina, Maria V. ;

Kudryashov, Nikolai A. .

APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (23) :9849-9853

[4] Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations [J].

Demina, Maria V. ;

Kudryashov, Nikolay A. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (03) :1127-1134

[5] From Laurent series to exact meromorphic solutions: The Kawahara equation [J].

Demina, Maria V. ;

Kudryashov, Nikolay A. .

PHYSICS LETTERS A, 2010, 374 (39) :4023-4029

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

Fan, EG .

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

[7] New exact solutions to the KdV-Burgers-Kuramoto equation [J].

Fu, ZT ;

Liu, SK ;

Liu, SD .

CHAOS SOLITONS & FRACTALS, 2005, 23 (02) :609-616

[8]

Gershenfield NeilA., 1999, NATURE MATH MODELING

[9] Modified simple equation method for nonlinear evolution equations [J].

Jawad, Anwar Ja'afar Mohamad ;

Petkovic, Marko D. ;

Biswas, Anjan .

APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (02) :869-877

[10] Modified Kudryashov method for finding exact solitary wave solutions of higher-order nonlinear equations [J].

Kabir, M. M. ;

Khajeh, A. ;

Aghdam, E. Abdi ;

Koma, A. Yousefi .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2011, 34 (02) :213-219

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