  We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal
trap potential in $D$ space dimensions and generalised to a nonlinearity of
order $2n+1$. For {\em attractive} coupling constants collapse of the particle
density occurs for $Dn\ge 2$ and typically to a $\delta$-function centered at
the origin of the trap. By introducing a new dynamical variable for the
spherically symmetric solutions we show that all such solutions are
self-similar close to the center of the trap. Exact self-similar solutions
occur if, and only if, $Dn=2$, and for this case of $Dn=2$ we exhibit an exact
but rather special D=1 analytical self-similar solution collapsing to a
$\delta$-function which however recovers and collapses periodically, while the
ordinary G-P equation in 2 space dimensions also has a special solution with
periodic $\delta$-function collapses and revivals of the density. The relevance
of these various results to attractive Bose-Einstein condensation in
spherically symmetric traps is discussed.
