Solutions to the nonlinear Schrِdinger equation with sequences of initial data converging to a Dirac mass

We study the nonlinear Schrِdinger equation with sequences of initial data that converge to a Dirac mass, and study the asymptotic behaviour of solutions. In doing so we find a connection to previously known long time asymptotics. We demonstrate a type of universality in the behaviour of solutions for real initial data, and we also show how this universality breaks down for examples of initial data that are not purely real.