Solutions to the nonlinear Schrodinger equation with Dirac mass initial data

We study the Nonlinear Schrodinger Equation Dirac mass initial data. We use scattering and inverse scattering theory to pose a Riemann Hilbert problem with a regularized reflection coefficient. We study the asymptotic behaviour of this RHP as the regularizing parameter tends to zero. We also establish asymptotic descriptions of solutions for sequences of initial data that converge to a Dirac mass, using a connection to previously known long time asymptotics