Appears in collection : Nonlinear Waves Trimester - May Conference

This talk is concerned with special properties of solutions to the IVP for the k-generalized KdV equation \pa_tu+\pa_x^3u+u^k \pa_xu=0 on the line. We shall discuss results concerning well posedness, unique continuation and propagaion of regularity, and compare them with similar results for other nonlinear dispersive models (in particular Benjamin Ono equation). This is joint work with P. Isaza and F. Linares