Stability or instability of solitary waves to double dispersion equation with quadratic-cubic nonlinearity

被引：3
|
作者：
Kolkovska, N. [1 ]
Dimova, M. [1 ]
Kutev, N. [1 ]
机构：
[1] BAS, Inst Math & Informat, Acad G Bonchev Str,Blvd 8, Sofia 1113, Bulgaria
来源：
MATHEMATICS AND COMPUTERS IN SIMULATION | 2017年 / 133卷
关键词：
Stability; Solitary waves; Double dispersion equation; GENERALIZED BOUSSINESQ EQUATION; GLOBAL EXISTENCE; BLOW-UP; BIOMEMBRANES;
D O I：
10.1016/j.matcom.2016.03.010
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
The solitary waves to the double dispersion equation with quadratic-cubic nonlinearity are explicitly constructed. Grillakis, Shatah and Strauss' stability theory is applied for the investigation of the orbital stability or instability of solitary waves to the double dispersion equation. An analytical formula, related to some conservation laws of the problem, is derived. As a consequence, the dependence of orbital stability or instability on the parameters of the problem is demonstrated. A complete characterization of the values of the wave velocity, for which the solitary waves to the generalized Boussinesq equation are orbitally stable or unstable, is given. In the special case of a quadratic nonlinearity our results are reduced to those known in the literature. (C) 2016 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：249 / 264
页数：16
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