On wave structures described by the generalized Kuramoto-Sivashinsky equation

被引：5
|
作者：
Kudryashov, Nikolay A. [1 ]
机构：
[1] Natl Res Nucl Univ MEPhI, Moscow Engn Phys Inst, Moscow 115409, Russia
来源：
APPLIED MATHEMATICS LETTERS | 2015年 / 49卷
基金：
俄罗斯科学基金会;
关键词：
Kuramoto-Sivashinsky equation; Painleve test; Painleve property; Elliptic solution; Exact solution; NONLINEAR DIFFERENTIAL-EQUATIONS; KAWAHARA EQUATION;
D O I：
10.1016/j.aml.2015.05.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The generalized Kuramoto-Sivashinsky equation is considered. The Painleve test is applied for studying this equation. It is shown that the generalized Kuramoto-Sivashinsky equation does not pass the Painleve test but has the expansion of the general solution in the Laurent series. As consequence the equation can have some exact solutions at additional conditions on the parameters of equation. Solitary wave and elliptic solutions of the generalized Kuramoto-Sivashinsky equation are found by means of expansion for solution in the Laurent series. It is shown that solutions obtained describe some structures in the medium with the dissipation and instability. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：84 / 90
页数：7
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