Painleve analysis and exact solutions of the fourth-order equation for description of nonlinear waves

被引：16

作者：

Kudryashov, Nikolay A. ^{[1
]}

机构：

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

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2015年 / 28卷 / 1-3期

基金：

俄罗斯科学基金会;

关键词：

Nonlinear differential equation; Nonlinear wave; Kuramoto-Sivashinsky equation; Painleve property; Painleve test; Exact solution; Logistic function; F-EXPANSION METHOD; EVOLUTION EQUATION; SOLITARY WAVES; SURFACE-WAVES; TANH METHOD; LIQUID;

D O I：

10.1016/j.cnsns.2015.03.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The fourth-order equation for description of nonlinear waves is considered. A few variants of this equation are studied. Painleve test is applied to investigate integrability of these equations. We show that all these equations are not integrable, but some exact solutions of these equations exist. Analytic solutions in closed-form of the equations are found. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：1 / 9

页数：9

共 50 条

[31] Positive solutions of the nonlinear fourth-order beam equation with three parameters
Liu, XL
Li, WT
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 303 (01) : 150 - 163
[32] Propagation of radius of analyticity for solutions to a fourth-order nonlinear Schrodinger equation
Getachew, Tegegne
Belayneh, Birilew
Tesfahun, Achenef
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (18) : 14867 - 14877
[33] Behavior of Solutions to a Fourth-Order Nonlinear Parabolic Equation with Logarithmic Nonlinearity
Jun Zhou
Applied Mathematics & Optimization, 2021, 84 : 191 - 225
[34] Global existence of small solutions for the fourth-order nonlinear Schrodinger equation
Aoki, Kazuki
Hayashi, Nakao
Naumkin, Pavel I.
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2016, 23 (06):
[35] Exponential time decay of solutions to a nonlinear fourth-order parabolic equation
A. Jüngel
G. Toscani
Zeitschrift für angewandte Mathematik und Physik ZAMP, 2003, 54 : 377 - 386
[36] Solutions for a fourth-order nonlinear parabolic equation describing Marangoni convection
Duan, Ning
APPLICABLE ANALYSIS, 2016, 95 (09) : 2081 - 2098
[37] Exponential time decay of solutions to a nonlinear fourth-order parabolic equation
Jüngel, A
Toscani, G
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2003, 54 (03): : 377 - 386
[38] EXISTENCE AND UNIQUENESS OF TRONQUEE SOLUTIONS OF THE FOURTH-ORDER JIMBO-MIWA SECOND PAINLEVE EQUATION
Joshi, Nalini
Morrison, Tegan
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (06) : 2005 - 2014
[39] ON THE PERIODIC SOLUTIONS OF A CERTAIN NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH-ORDER
Tunc, Cemil
BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES, 2008, 3 (02): : 315 - 322
[40] ON THE EXISTENCE OF PERIODIC SOLUTIONS TO A CERTAIN FOURTH-ORDER NONLINEAR DIFFERENTIAL EQUATION
Cemil Tun
Annals of Applied Mathematics, 2009, (01) : 8 - 12

← 1 2 3 4 5 →