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Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 71 (2005) 026307
Nonlinear Dynamics of Short Travelling Capillary-gravity Waves
H. C. Borzi, R.A Kraenkel, Miguel Manna1, A. Pereira2

We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-waves dynamics, we show that this system posseses (1+1) travelling waves solutions for almost all the values of the Bond number B (the special case B=1/3 is not studied). These waves become singular when their amplitude is larger than a threshold value, related to the velocity of the wave. The limit angle at the crest is then calculated. The stability of a wave train is also studied via a Benjamin-Feir modulational analysis.
1 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
2 :  PMT - Laboratoire de Physique Mathématique et Théorique
Science non linéaire/Formation de Structures et Solitons
capillary waves – gravity waves – flow instability