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Physica D: Nonlinear Phenomena 211 (2005) 377-390
Theory of small aspect ratio waves in deep water
A. Kraenkel, J. Leon1, M. A. Manna1

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution.
1 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
Science non linéaire/Formation de Structures et Solitons

Science non linéaire/Systèmes Solubles et Intégrables
Water waves – Asymptotic methods – Nonlinear dynamics
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