Abenda, SimonettaGrava, TamaraKlein, Christian2010-02-052011-09-072010-02-052011-09-072010-02-05https://openscience.sissa.it/handle/1963/3840The small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture....613403 bytesapplication/pdfen-USPreprint