A numerical study of the stability of solitary waves of the Bona-Smith family of Boussinesq systems. (English) Zbl 1135.35070
Summary: In this paper we study, some aspects of stability of solitary-wave solutions of the Bona-Smith systems of equations from a numerical point of view. These systems are a family of Boussinesq-type equations, 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.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76B25 | Solitary waves for incompressible inviscid fluids |
| 35B25 | Singular perturbations in context of PDEs |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 35Q51 | Soliton equations |
| 35B35 | Stability in context of PDEs |
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