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Abstract
When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two and threedimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravitycapillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the DirichlettoNeumann operator. This approximation has been proved to be very accurate for both two and threedimensional computations of fully localized gravitycapillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles.
Original language  English 

Article number  20130537 
Journal  Proceedings of the Royal Society of London Series A  Mathematical Physical and Engineering Sciences 
Volume  470 
Issue number  2161 
Early online date  30 Oct 2013 
DOIs  
Publication status  Published  Jan 2014 
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Dive into the research topics of 'Transversally periodic solitary gravitycapillary waves'. Together they form a unique fingerprint.Projects
 1 Finished

Nonlinear Hydroelastic Waves with Applications to Ice Sheets
Milewski, P.
Engineering and Physical Sciences Research Council
12/11/12 → 11/11/15
Project: Research council