  We make two observations concerning the generalised Korteweg de Vries
equation $u_t + u_{xxx} = \mu (|u|^{p-1} u)_x$. Firstly we give a scaling
argument that shows, roughly speaking, that any quantitative scattering result
for $L^2$-critical equation ($p=5$) automatically implies an analogous
scattering result for the $L^2$-critical nonlinear Schr\"odinger equation $iu_t
+ u_{xx} = \mu |u|^4 u$. Secondly, in the defocusing case $\mu > 0$ we present
a new dispersion estimate which asserts, roughly speaking, that energy moves to
the left faster than the mass, and hence strongly localised soliton-like
behaviour at a fixed scale cannot persist for arbitrarily long times.
