Transverse instability of gravity-capillary line solitary water waves

Transverse instability of gravity-capillary line solitary water waves

The gravity-capillary water-wave problem concerns the irrotational flow of a perfect fluid in a domain bounded below by a rigid bottom and above by a free surface under the influence of gravity and surface tension. In the case of large surface tension the system has a travelling line solitary-wave solution for which the free surface has a localised profile in the direction of propagation and is...

Transverse Instability of the Line Solitary Water-waves

We prove the linear and nonlinear instability of the line solitary water waves with respect to transverse perturbations.

Three-dimensional Solitary Gravity-capillary Water Waves

The existence of solitary-wave solutions to the three-dimensional water-wave problem with strong surface-tension effects is predicted by the KP-I model equation. The term solitary wave describes any solution which has a pulse-like profile in its direction of propagation, and the KP-I equation admits explicit solutions for three different types of solitary wave. A line solitary wave is spatially...

A plethora of generalised solitary gravity-capillary water waves

Nonlinear three-dimensional gravity–capillary solitary waves

E. I. PARAU, J.­M. VANDEN­BROECK and M. J. COOKER Journal of Fluid Mechanics / Volume 536 / August 2005, pp 99 ­ 105 DOI: 10.1017/S0022112005005136, Published online: 26 July 2005 Link to this article: http://journals.cambridge.org/abstract_S0022112005005136 How to cite this article: E. I. PARAU, J.­M. VANDEN­BROECK and M. J. COOKER (2005). Nonlinear three­dimensional gravity–capillary solitary...