Journal of Nonlinear Science

, Volume 17, Issue 6, pp 569–607

A Numerical Study of the Stability of Solitary Waves of the Bona–Smith Family of Boussinesq Systems

Authors

    • Mathematics DepartmentUniversity of Athens
    • Institute of Applied and Computational MathematicsF.O.R.T.H.
  • A. Durán
    • Applied Mathematics Department, Faculty of SciencesUniversity of Valladolid
  • M. A. López-Marcos
    • Applied Mathematics Department, Faculty of SciencesUniversity of Valladolid
  • D. E. Mitsotakis
    • Mathematics DepartmentUniversity of Athens
    • Institute of Applied and Computational MathematicsF.O.R.T.H.
Article

DOI: 10.1007/s00332-007-9004-8

Cite this article as:
Dougalis, V.A., Durán, A., López-Marcos, M.A. et al. J Nonlinear Sci (2007) 17: 569. doi:10.1007/s00332-007-9004-8

Abstract

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.

Keywords

Boussinesq systemsStability of solitary waves

Mathematics Subject Classification (2000)

35Q5365M6076B25

Copyright information

© Springer Science+Business Media, LLC 2007