The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom

. The goal of this work is to investigate, analytically and numerically, the dynamics of gravity water waves with the effects of the small surface tension and the bottom topography taken into account. Using a third-order perturbative approach of the Boussinesq equation, we obtain a new third-order p...

Full description

Saved in:
Bibliographic Details
Published in:European physical journal plus 2017-10, Vol.132 (10), p.410, Article 410
Main Authors: Fokou, M., Kofané, T. C., Mohamadou, A., Yomba, E.
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Boussinesq equations
Complex Systems
Condensed Matter Physics
Gravity
Korteweg-Devries equation
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Shallow water
Solitary waves
Surface tension
Theoretical
Water waves
Wave propagation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:. The goal of this work is to investigate, analytically and numerically, the dynamics of gravity water waves with the effects of the small surface tension and the bottom topography taken into account. Using a third-order perturbative approach of the Boussinesq equation, we obtain a new third-order perturbed Korteweg-de Vries (KdV) equation which includes nonlinear, dispersive, nonlocal and mixed nonlinear-dispersive terms, describing shallow water waves with a non-flat bottom and the surface tension. We show by numerical simulations, for various bottom shapes, that this new third-order perturbed KdV equation can support the propagation of solitary waves, whose profiles strongly depend on the surface tension. In particular, we show that the instability observed in the numerical simulation can be suppressed by the inclusion of small surface tension.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/i2017-11709-0