Appears in collection : Recent trends in nonlinear evolution equations / Nouvelles perspectives sur les équations d'évolution non linéaires

The one dimensional half wave equation is an interesting example of a nonlinear wave equation with vanishing dispersion, displaying arbitrarily small mass solitons. I will discuss how, in some resonant regime, the interaction of two such solitons leads to long time transition to high frequencies. This talk is issued from a jointwork with Enno Lenzmann, Oana Pocovnicu and Pierre Raphael.