A numerical study of the stability of solitary waves of the Bona-Smith family of Boussinesq systems

被引：23
|
作者：
Dougalis, V. A. [1 ,2 ]
Duran, A. [3 ]
Lopez-Marcos, M. A. [3 ]
Mitsotakis, D. E. [1 ,2 ]
机构：
[1] Univ Athens, Dept Math, Zografos 15784, Greece
[2] FORTH, Inst Appl & Comp Math, Iraklion, Greece
[3] Univ Valladolid, Fac Sci, Dept Appl Math, E-47011 Valladolid, Spain
来源：
JOURNAL OF NONLINEAR SCIENCE | 2007年 / 17卷 / 06期
关键词：
boussinesq systems; stability of solitary waves;
D O I：
10.1007/s00332-007-9004-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study, from a numerical point of view, some aspects of stability of solitary-wave solutions of the Bona-Smith systems of equations. These systems are a family of Boussinesq-type equations and were originally proposed for modelling the two-way propagation of one-dimensional long waves of small amplitude in an open channel of water of constant depth. We study numerically the behavior of solitary waves of these systems under small and large perturbations with the aim of illuminating their long-time asymptotic stability properties and, in the case of large perturbations, examining, among other, phenomena of possible blow-up of the perturbed solutions in finite time.
引用
收藏
页码：569 / 607
页数：39
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