University of Prince Edward Island, June 5 - 8, 2015
Recent numerical simulations of an $L^2$-supercritical generalization to the DNLS provide evidence of finite time singularities. Near the singularity, the solution is described by a universal profile that solves a nonlinear elliptic eigenvalue problem depending only on the strength of the nonlinearity. In this work, we use asymptotic analysis to describe the deformation of the profile and the parameters in the limit of criticality. We compare our results to a numerical integration of the problem. This is a joint work with G. Simpson and C. Sulem.