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Abstract
The nonlinear Schrödinger (NLS) equation describes the modulational limit of many surface water wave problems. Dark solitary waves of the NLS equation asymptote to a constant in the far field and have a localized decrease to zero amplitude at the origin, corresponding to water wave solutions that asymptote to a uniform periodic Stokes wave in the far field and decreasing oscillations near the origin. It is natural to ask whether these dark solitary waves can be found in the irrotational Euler equations. In this paper, we find such solutions in the context of flexuralgravity waves, which are often used as a model for waves in icecovered water. This is a situation in which the NLS equation predicts steadily travelling dark solitons. The solution branches of dark solitons are continued, and one branch leads to fully localized solutions at large amplitudes.
Original language  English 

Article number  20120485 
Journal  Proceedings of the Royal Society A 
Volume  469 
Issue number  2150 
Early online date  28 Nov 2012 
DOIs  
Publication status  Published  Feb 2013 
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 1 Finished

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